1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft


 Aubrey Marshall
 2 years ago
 Views:
Transcription
1 2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite skill in geometry and real world applications. Units of Length American Units of Length. Facts relating common units of length. 1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Change 48 inches to feet. EXAMPLE 1. Change 24 inches to feet. Solution. Multiply by the conversion factor 1 ft/12 in. Answer: 4 feet 24 in = 24 in 1 Multiplicative Identity Property. 1ft = 24 in 12 in Replace 1 with 1 ft/12 in. 1ft =24 in 12 in Cancel common unit. = 24 1 ft 12 Multiply fractions. =2ft Simplify. Hence, 24 inches equals 2 feet. A summary of conversion factors for units of length is given in Table 6.1. Convert Conversion Factor Convert Conversion Factor feet to inches 12 in/1 ft inches to feet 1 ft/12 in yards to feet 3ft/1yd feet to yards 1yd/3ft miles to feet 5280ft/1 mi feet to miles 1 mi/5280 ft Table 6.1: Conversion factors for units of length. Some conversions require more than one application of a conversion factor. Change 8 yards to inches. EXAMPLE 2. Change 4 yards to inches.
2 6A. APPLICATIONS 3 Solution. We multiply by a chain of conversion factors, the first to change yards to feet, the second to change feet to inches. 4yd=4yd 3ft 12 in 1yd 1ft Multiply by conversion factors. =4 yd 3 ft 12 in 1 yd 1 ft Cancel common units. = in 1 1 Multiply fractions. = 144 in Simplify. Hence, 4 yards equals 144 inches. Answer: 288 inches Applications Geometry Solving many real world problems require some geometry. We start our review with the perimeter of a polygon, in particular, a rectangle. Perimeter of a Polygon. In geometry a polygon is a plane figure made up of a closed path of a finite sequence of segments. The segments are called the edges or sides of the polygon and the points where two edges meet are called the vertices of the polygon. The perimeter of any polygon is the sum of the lengths of its sides. EXAMPLE 3. A quadrilateral (four sides) is a rectangle if all four of its A rectangle has length 12 angles are right angles. It can be shown that the opposite sides of a rectangle must be equal. Find the perimeter of the rectangle shown below, where the meters and width 8 meters. Find its perimeter. sides of the rectangle are measured in meters. 3m 5m Solution. To find the perimeter of the rectangle, find the sum of the four sides. Because opposite sides have the same length, we have two sides of length 5 meters and two sides of length 3 meters. Hence, Perimeter = = 16.
3 4 MODULE 6. GEOMETRY AND UNIT CONVERSION Answer: 40 meters Thus, the perimeter of the rectangle is 16 meters. Note that the perimeter of a rectangle can be found by summing twice the length and width of the sides. This is given by the formula P =2L +2W. Application Area Consider the rectangle shown in Figure 6.1. The length of this rectangle is four inches (4 in) and the width is three inches (3 in). 3 in One square inch (1 in 2 ) 4 in Figure 6.1: A rectangle with length 4 inches and width 3 inches. To find the area of the figure, we can count the individual units of area (in 2 ) that make up the area of the rectangle, twelve square inches (12 in 2 ) in all. However, it is much faster to multiply the number of squares in each row by the number of squares in each column: 4 3 = 12 square inches. The argument presented above leads to the rule for finding the area ofa rectangle. Area of a Rectangle. LetL and W represent the length and width of a rectangle, respectively. L W W L To find the area of the rectangle, calculate the product of the length and width. That is, if A represents the area of the rectangle, then the area of the rectangle is given by the formula A = LW.
4 6A. APPLICATIONS 5 ou Try It! EXAMPLE 4. A rectangle has width 5 feet and length 12 feet. Find the A rectangle has width 17 area of the rectangle. inches and length 33 inches. Solution. Substitute L =12ftandW = 5 ft into the area formula. Find the area of the rectangle. A = LW =(12ft)(5ft) =60ft 2 Hence, the area of the rectangle is 60 square feet. Answer: 561 square inches. Volume of a Prism The natural next step is to look at the volume of a solid. The first one we consider is the rectangular solid or prism. EXAMPLE 5. Pictured below is a rectangular prism. The surface area of the prism pictured in this example is given by the following formula: S =2(WH + LH + LW ) H If L =12,W =4,andH =6 feet, respectively, calculate the surface area. L W The volume of the rectangular prism is given by the formula V = LW H, where L is the length, W is the width, and H is the height of the rectangular prism. Find the volume of a rectangular prism having length 12 feet, width 4 feet, and height 6 feet. Solution. Following Tips for Evaluating Algebraic Expressions, first replace all occurrences of of L, W,andH in the formula V = LW H
5 6 MODULE 6. GEOMETRY AND UNIT CONVERSION with open parentheses. ( )( )( ) V = Next, substitute 12 ft for L, 4ftforW,and6ftforH and simplify. V = ( 12 ft )( 4ft )( 6ft ) =288ft 3 Answer: 288 square feet. Hence, the volume of the rectangular prism is 288 cubic feet. We can simplify a number of formulas by combining like terms. A regular hexagon has six equal sides, each with length x. Find its perimeter in terms of x. EXAMPLE 6. Find a formula for the perimeter P of the (a) rectangle and (b) square pictured below. Simplify your answer as much as possible. L s W W s s L Solution. The perimeter of any polygonal figure is the sum of the lengths of its sides. a) To find the perimeter P of the rectangle, sum its four sides. P = L + W + L + W. s Combine like terms. P =2L +2W. b) To find the perimeter P of the square, sum its four sides. P = s + s + s + s. Combine like terms. P =4s. Answer: P =6x Sometimes a variable in a formula is given in terms of a another variable. The following example illustrates replacing a variable with an expression containing another (related) variable.
6 6A. APPLICATIONS 7 ou Try It! EXAMPLE 7. The length of a rectangle is three feet longer than twice its width. Find the perimeter P of the rectangle in terms of only its width. Solution. From the previous problem, the perimeter of the rectangle is given by P =2L +2W, (6.1) where L and W are the length and width of the rectangle, respectively. This equation gives the perimeter in terms of its length and width, but we re asked to get the perimeter in terms of only its width. However, we re also given the fact that the length is three feet longer than twice the width. That is, the length is described in terms of the width. The length L of a rectangle is 5 meters longer than twice its width W. Find the perimeter P of the rectangle in terms of its width W. Length is Three Feet longer than Twice the Width L = 3 + 2W Because L =3+2W, we can replace L with 3 + 2W in the perimeter formula. P =2L +2W P =2(3+2W )+2W Apply the distributive property, then combine like terms. P =6+4W +2W P =6+6W. This last equation gives the perimeter P in terms of only its width W. Answer: P =6W +10 Consecutive Integers In the application of geometry to solve real world problems, the lengths of geometric figures may be expressed by algebraic expressions. Consecutive Integers. Let k represent an integer. The next consecutive integer is the integer k +1. Thus, if k is an integer, then k + 1 is the next integer, k + 2 is the next integer after that, and so on.
7 8 MODULE 6. GEOMETRY AND UNIT CONVERSION The three sides of a triangle are consecutive integers and the perimeter is 57 centimeters. Find the measure of each side of the triangle. EXAMPLE 8. The three sides of a triangle are consecutive integers and the perimeter is 72 inches. Find the measure of each side of the triangle. Solution. We follow the Requirements for Word Problem Solutions. 1. Set up a Variable Dictionary. In this case, a carefully labeled diagram is the best way to indicate what the unknown variable represents. k +2 k k +1 In our schematic diagram, we ve labeled the three sides of the triangle with expressions representing the consecutive integers k, k +1, and k Set up an Equation. To find the perimeter P of the triangle, sum the three sides. P = k +(k +1)+(k +2) However, we re given the fact that the perimeter is 72 inches. Thus, 72 = k +(k +1)+(k +2) 3. Solve the Equation. On the right, regroup and combine like terms. Now, solve for k. 72 = 3k =3k +3 3 Subtract 3 from both sides. 69 = 3k Simplify = 3k 3 Divide both sides by = k Simplify. 4. Answer the Question. We ve only found one side, but the question asks for the measure of all three sides. However, the remaining two sides can be found by substituting 23 for k into the expressions k +1andk +2. k +1=23+1 and k +2=23+2 =24 =25 Hence, the three sides measure 23 inches, 24 inches, and 25 inches.
8 6A. APPLICATIONS 9 5. Look Back. Does our solution make sense? Well, the three sides are certainly consecutive integers, and their sum is 23 inches + 24 inches + 25 inches = 72 inches, which was the given perimeter. Therefore, our solution is correct. Answer: 18, 19, and 20 cm Area of a Parallelogram Area of a Parallelogram. A parallelogram having base b and height h has area A = bh. That is, to find the area of a parallelogram, take the product of its base and height. EXAMPLE 9. Find the area of the parallelogram pictured below. 5/3 ft The base of a parallelogram measures 14 inches. The height is 8/7 of an inch. What is the area of the parallelogram? 6ft Solution. The area of the parallelogram is equal to the product of its base and height. That is, A = bh =(6ft) ( ) 5 3 ft Area formula for parallelogram. Substitute: 6 ft for b, 5/3 ft for h. = 30 3 ft2. Multiply numerators and denominators. =10ft 2. Divide. Thus, the area of the parallelogram is 10 square feet. Answer: 16 square inches Area of a Triangle Area of a Triangle. A triangle having base b and height h has area A = (1/2)bh. That is, to find the area of a triangle, take onehalf the product of the base and height.
9 10 MODULE 6. GEOMETRY AND UNIT CONVERSION The base of a triangle measures 15 meters. The height is 12 meters. What is the area of the triangle? EXAMPLE 10. Find the area of the triangle pictured below. 6cm 13 cm Solution. To find the area of the triangle, take onehalf the product of the base and height. A = 1 2 bh Area of a triangle formula. = 1 (13 cm)(6 cm) Substitute: 13 cm for b, 6cmforh cm2 = 2 =39cm 2. Multiply numerators; multiply denominators. Simplify. Answer: 90 square meters Therefore, the area of the triangle is 39 square centimeters. Area of a Trapezoid. Area of a Trapezoid. A trapezoid with bases b 1 and b 2 and height h has area A = 1 2 h (b 1 + b 2 ). That is, to find the area, sum the bases, multiply by the height, and take onehalf of the result. A trapezoid has bases measuring 6 and 15 feet, respectively. The height of the trapezoid is 5 feet. Find the area of the trapezoid. EXAMPLE 11. Find the area of the trapezoid pictured below in 3 in in
10 6A. APPLICATIONS 11 Solution. The formula for the area of a trapezoid is A = 1 2 h (b 1 + b 2 ) Substituting the given bases and height, we get A = 1 ( 2 (3) 4 1 ) Simplify the expression inside the parentheses first. Change mixed fractions to improper fractions, make equivalent fractions with a common denominator, then add. A = 1 ( 17 2 (3) ) 2 = 1 ( 17 2 (3) ) 2 2 = 1 ( 17 2 (3) ) 4 = 1 2 ( 3 1 Multiply numerators and denominators. = 81 8 )( 27 4 This improper fraction is a perfectly good answer, but let s change this result to a mixed fraction (81 divided by 8 is 10 with a remainder of 1). Thus, the area of the trapezoid is ) A =10 1 square inches. 8 Answer: square feet Height of a Triangle EXAMPLE 12. The area of a triangle is 20 square inches. If the length of The area of a triangle is 161 the base is 2 1 square feet. If the base of 2 inches, find the height (altitude) of the triangle. the triangle measures Solution. We follow the Requirements for Word Problem Solutions. feet, find the height of the triangle.
11 12 MODULE 6. GEOMETRY AND UNIT CONVERSION 1. Set up a Variable Dictionary. Our variable dictionary will take the form of a well labeled diagram. h in 2. Set up an Equation. The area A of a triangle with base b and height h is A = 1 2 bh. Substitute A =20andb = = 1 2 ( 2 1 ) h Solve the Equation. Change the mixed fraction to an improper fraction, then simplify. 20 = 1 ( 2 1 ) h Original equation = 1 ( ) 5 h Mixed to improper: = 5 2. ( 1 20 = 2 5 ) h Associative property = 5 4 h Multiply: = 5 4. Now, multiply both sides by 4/5 and solve. 4 5 (20) = 4 ( ) h Multiply both sides by 4/ = h Simplify: (20) = 16 5 and =1. 4. Answer the Question. The height of the triangle is 16 inches.
12 6A. APPLICATIONS Look Back. If the height is 16 inches and the base is area is A = 1 ( 2 1 ) (16) 2 2 inches, then the = = (5) ( ) = (2) (2) = =20 This is the correct area (20 square inches), so our solution is correct. Answer: 8 feet Circumference of a Circle EXAMPLE 13. Find the circumference of a circle given its radius is 12 feet. Solution. The circumference of the circle is given by the formula C = πd, or, because d =2r, C =2πr. Substitute 12 for r. C =2πr =2π(12) = 24π Therefore, the circumference of the circle is exactly C = 24π feet. We can approximate the circumference by entering an approximation for π. Let s use π Note: The symbol is read approximately equal to. Find the radius of a circle having radius 14 inches. Use π 3.14 C =24π 24(3.14) feet It is important to understand that the solution C = 24π feet is the exact circumference, while C feet is only an approximation. Answer: inches Area of a Circle EXAMPLE 14. Find the area of a circle having a diameter of 12.5 meters. Use 3.14 for π and round the answer for the area to the nearest tenth of a square meter. Find the area of a circle having radius 12.2 centimeters. Use π 3.14
13 Answer: cm 2 14 MODULE 6. GEOMETRY AND UNIT CONVERSION Solution. The diameter is twice the radius. Substitute 12.5 for d and solve for r. d =2r 12.5 = 2r Substitute 12.5 for d = 2r 2 2 Divide both sides by = r Simiplify. Hence, the radius is 6.25 meters. To find the area, use the formula A = πr 2 and substutite: 3.14 for π and 6.25 for r. A =(3.14)(6.25) 2 Substitute: 3.14 for π, 6.25 for r. =(3.14)( ) Square first: (6.25) 2 = = Multiply: (3.14)( ) = Hence, the approximate area of the circle is A = square meters. To round to the nearest tenth of a square meter, identify the rounding digit and the test digit. Rounding digit Test digit Because the test digit is greater than or equal to 5, add 1 to the rounding digit and truncate. Thus, correct to the nearest tenth of a square meter, the area of the circle is approximately A 122.7m 2. The Pythagorean Theorem We now state one of the most ancient theorems of mathematics, the Pythagorean Theorem. Pythagorean Theorem. Let c represent the length of the hypotenuse of a right triangle, and let a and b represent the lengths of its legs, as pictured in the image that follows.
14 6A. APPLICATIONS 15 c a b The relationship involving the legs and hypotenuse of the right triangle, given by a 2 + b 2 = c 2, is called the Pythagorean Theorem. EXAMPLE 15. Given the following right triangle, find the exact length of the missing side. 7 The hypotenuse and one leg of a right triangle measure 9 and 7 inches, respectively. Find the length of the remaining leg. x 12 Solution. Note that the hypotenuse (across from the right angle) has length 12. This quantity should lie on one side of the Pythagorean equation all by itself. The sum of the squares of the legs go on the other side. Hence, Solve the equation for x. x =12 2 x 2 +49=144 Exponents first: 7 2 =49and12 2 =144. x = x 2 =95 Subtract 49 from both sides. Simplify both sides. x = 95 Take the nonnegative square root of 95. Hence, the exact length of the missing side is 95. Answer: 32 inches
Quick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 17 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationName Date Time. STUDY LINK 8 13 Unit 9: Family Letter. Please keep this Family Letter for reference as your child works through Unit 9.
Name Date Time STUDY LINK Unit 9: Family Letter More about Variables, Formulas, and Graphs You may be surprised at some of the topics that are covered in Unit 9. Several of them would be traditionally
More informationArea of Parallelograms, Triangles, and Trapezoids (pages 314 318)
Area of Parallelograms, Triangles, and Trapezoids (pages 34 38) Any side of a parallelogram or triangle can be used as a base. The altitude of a parallelogram is a line segment perpendicular to the base
More informationName: Class: Date: Geometry Chapter 3 Review
Name: Class: Date: ID: A Geometry Chapter 3 Review. 1. The area of a rectangular field is 6800 square meters. If the width of the field is 80 meters, what is the perimeter of the field? Draw a diagram
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationTeacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.
Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 91.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles
More informationCharacteristics of the Four Main Geometrical Figures
Math 40 9.7 & 9.8: The Big Four Square, Rectangle, Triangle, Circle Pre Algebra We will be focusing our attention on the formulas for the area and perimeter of a square, rectangle, triangle, and a circle.
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More informationSolutions Section J: Perimeter and Area
Solutions Section J: Perimeter and Area 1. The 6 by 10 rectangle below has semicircles attached on each end. 6 10 a) Find the perimeter of (the distance around) the figure above. b) Find the area enclosed
More informationTopic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = =  10.
Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign + 6 + + 5 = + 118 +  2 =  10 Different signs: Subtract & take sign of larger value + 9 +  5 = + 46
More informationPERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures.
PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various twodimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the
More informationof surface, 569571, 576577, 578581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433
Absolute Value and arithmetic, 730733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property
More informationArea LongTerm Memory Review Review 1
Review 1 1. To find the perimeter of any shape you all sides of the shape.. To find the area of a square, you the length and width. 4. What best identifies the following shape. Find the area and perimeter
More informationLine AB (no Endpoints) Ray with Endpoint A. Line Segments with Endpoints A and B. Angle is formed by TWO Rays with a common Endpoint.
Section 8 1 Lines and Angles Point is a specific location in space.. Line is a straight path (infinite number of points). Line Segment is part of a line between TWO points. Ray is part of the line that
More informationA = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height
Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side
More information1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B. Whole Numbers
Whole Numbers Scope and Sequence for Primary Mathematics, U.S. Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced or specifically addressed. Understand
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationSixth Grade Math Pacing Guide Page County Public Schools MATH 6/7 1st Nine Weeks: Days Unit: Decimals B
Sixth Grade Math Pacing Guide MATH 6/7 1 st Nine Weeks: Unit: Decimals 6.4 Compare and order whole numbers and decimals using concrete materials, drawings, pictures and mathematical symbols. 6.6B Find
More informationArea of Parallelograms (pages 546 549)
A Area of Parallelograms (pages 546 549) A parallelogram is a quadrilateral with two pairs of parallel sides. The base is any one of the sides and the height is the shortest distance (the length of a perpendicular
More informationReview for Final  Geometry B
Review for Final  Geometry B Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A model is made of a car. The car is 4 meters long and the model is 7 centimeters
More informationLesson 7: Using Formulas
Lesson 7: Using Formulas Steps for Solving Problems Using a Formula 1. 2. 3. 4. Example 1 Using the formula: Density = mass/volume or D = m/v Find the density of a rock that has a volume of 20 ml with
More information124 Volumes of Prisms and Cylinders. Find the volume of each prism.
Find the volume of each prism. 3. the oblique rectangular prism shown at the right 1. The volume V of a prism is V = Bh, where B is the area of a base and h is the height of the prism. If two solids have
More informationEXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS
To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires
More informationRIT scores between 191 and 200
Measures of Academic Progress for Mathematics RIT scores between 191 and 200 Number Sense and Operations Whole Numbers Solve simple addition word problems Find and extend patterns Demonstrate the associative,
More informationGeometry Unit 7 (Textbook Chapter 9) Solving a right triangle: Find all missing sides and all missing angles
Geometry Unit 7 (Textbook Chapter 9) Name Objective 1: Right Triangles and Pythagorean Theorem In many geometry problems, it is necessary to find a missing side or a missing angle of a right triangle.
More informationFifth Grade. Scope & Sequence of Lessons. by lesson number
Scope & Sequence of Lessons by lesson number PLACE VALUE AND COUNTING Place value 1 Recognizing numbers less than a million 65 Recognizing tenths and hundredths places 80 Recognizing numbers up through
More informationGeo  CH9 Practice Test
Geo  H9 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. Find the area of the parallelogram. a. 35 in 2 c. 21 in 2 b. 14 in 2 d. 28 in 2 2.
More informationGeometry Concepts. Figures that lie in a plane are called plane figures. These are all plane figures. Triangle 3
Geometry Concepts Figures that lie in a plane are called plane figures. These are all plane figures. Polygon No. of Sides Drawing Triangle 3 A polygon is a plane closed figure determined by three or more
More informationVOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region.
Math 6 NOTES 7.5 Name VOLUME of Rectangular Prisms Volume is the measure of occupied by a solid region. **The formula for the volume of a rectangular prism is:** l = length w = width h = height Study Tip:
More information122 Surface Areas of Prisms and Cylinders. 1. Find the lateral area of the prism. SOLUTION: ANSWER: in 2
1. Find the lateral area of the prism. 3. The base of the prism is a right triangle with the legs 8 ft and 6 ft long. Use the Pythagorean Theorem to find the length of the hypotenuse of the base. 112.5
More informationFCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST. Mathematics Reference Sheets. Copyright Statement for this Assessment and Evaluation Services Publication
FCAT FLORIDA COMPREHENSIVE ASSESSMENT TEST Mathematics Reference Sheets Copyright Statement for this Assessment and Evaluation Services Publication Authorization for reproduction of this document is hereby
More informationSierra Verde STEM Academy 8 th Grade Summer Math Packet
Sierra Verde STEM Academy 8 th Grade Summer Math Packet Dear Incoming 8 th Graders, Please complete this summer math packet prior to the beginning of the 20152016 school year. The purpose of the math
More information83 Perimeter and Circumference
Learn to find the perimeter of a polygon and the circumference of a circle. 83 Perimeter Insert Lesson and Title Circumference Here perimeter circumference Vocabulary The distance around a geometric figure
More informationMATH STUDENT BOOK. 7th Grade Unit 9
MATH STUDENT BOOK 7th Grade Unit 9 Unit 9 Measurement and Area Math 709 Measurement and Area Introduction 3 1. Perimeter 5 Perimeter 5 Circumference 11 Composite Figures 16 Self Test 1: Perimeter 24 2.
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationGeometry. Geometry is the study of shapes and sizes. The next few pages will review some basic geometry facts. Enjoy the short lesson on geometry.
Geometry Introduction: We live in a world of shapes and figures. Objects around us have length, width and height. They also occupy space. On the job, many times people make decision about what they know
More informationTallahassee Community College PERIMETER
Tallahassee Community College 47 PERIMETER The perimeter of a plane figure is the distance around it. Perimeter is measured in linear units because we are finding the total of the lengths of the sides
More informationComposite Figures. Learning Objectives. PreActivity
Section 3.6 Prectivity Preparation Composite Figures Leisure activities often include the use of different combinations of basic shapes. Below are some examples of how we might use basic shapes in complex
More informationSurface Area of Rectangular & Right Prisms Surface Area of Pyramids. Geometry
Surface Area of Rectangular & Right Prisms Surface Area of Pyramids Geometry Finding the surface area of a prism A prism is a rectangular solid with two congruent faces, called bases, that lie in parallel
More information111 Areas of Parallelograms and Triangles. Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary.
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 2. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. Each pair of opposite
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More information124 Volumes of Prisms and Cylinders. Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h
Find the volume of each prism. The volume V of a prism is V = Bh, where B is the area of a base and h The volume is 108 cm 3. The volume V of a prism is V = Bh, where B is the area of a base and h the
More informationGrade 3 Math Expressions Vocabulary Words
Grade 3 Math Expressions Vocabulary Words Unit 1, Book 1 Place Value and MultiDigit Addition and Subtraction OSPI words not used in this unit: add, addition, number, more than, subtract, subtraction,
More informationIntegrated Algebra: Geometry
Integrated Algebra: Geometry Topics of Study: o Perimeter and Circumference o Area Shaded Area Composite Area o Volume o Surface Area o Relative Error Links to Useful Websites & Videos: o Perimeter and
More informationName: Perimeter and area November 18, 2013
1. How many differently shaped rectangles with whole number sides could have an area of 360? 5. If a rectangle s length and width are both doubled, by what percent is the rectangle s area increased? 2.
More informationMath Content
20122013 Math Content PATHWAY TO ALGEBRA I Unit Lesson Section Number and Operations in Base Ten Place Value with Whole Numbers Place Value and Rounding Addition and Subtraction Concepts Regrouping Concepts
More informationFundamentals of Geometry
10A Page 1 10 A Fundamentals of Geometry 1. The perimeter of an object in a plane is the length of its boundary. A circle s perimeter is called its circumference. 2. The area of an object is the amount
More informationMeasurement and Geometry: Perimeter and Circumference of Geometric Figures
OpenStaxCNX module: m35022 1 Measurement and Geometry: Perimeter and Circumference of Geometric Figures Wade Ellis Denny Burzynski This work is produced by OpenStaxCNX and licensed under the Creative
More informationName: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:
Name: Date: Geometry Honors 20132014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 16 HW: Pgs: 710 DAY 2: SWBAT: Calculate the Volume
More information126 Surface Area and Volumes of Spheres. Find the surface area of each sphere or hemisphere. Round to the nearest tenth. SOLUTION: ANSWER: 1017.
Find the surface area of each sphere or hemisphere. Round to the nearest tenth. 3. sphere: area of great circle = 36π yd 2 We know that the area of a great circle is r.. Find 1. Now find the surface area.
More informationTopic: Integers. Addition Subtraction Multiplication Division Same signs: Add & keep sign = =  10.
Topic: Integers Examples: Addition Subtraction Multiplication Division Same signs: Add & keep sign + 6 + + 5 = +  8 +  2 =  0 Different signs: Subtract & take sign of larger value + 9 +  5 = + 46
More informationMath 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.
Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used
More informationGeometry Review. Here are some formulas and concepts that you will need to review before working on the practice exam.
Geometry Review Here are some formulas and concepts that you will need to review before working on the practice eam. Triangles o Perimeter or the distance around the triangle is found by adding all of
More informationIndividual Round Arithmetic
Individual Round Arithmetic (1) A stack of 100 nickels is 6.25 inches high. To the nearest $.01, how much would a stack of nickels 8 feet high be worth? 8 feet = 8 12 inches. Dividing 96 inches by 6.25
More informationArea of a triangle: The area of a triangle can be found with the following formula: You can see why this works with the following diagrams:
Area Review Area of a triangle: The area of a triangle can be found with the following formula: 1 A 2 bh or A bh 2 You can see why this works with the following diagrams: h h b b Solve: Find the area of
More informationSect 8.3 Quadrilaterals, Perimeter, and Area
186 Sect 8.3 Quadrilaterals, Perimeter, and Area Objective a: Quadrilaterals Parallelogram Rectangle Square Rhombus Trapezoid A B E F I J M N Q R C D AB CD AC BD AB = CD AC = BD m A = m D m B = m C G H
More informationMath Help and Additional Practice Websites
Name: Math Help and Additional Practice Websites http://www.coolmath.com www.aplusmath.com/ http://www.mathplayground.com/games.html http://www.ixl.com/math/grade7 http://www.softschools.com/grades/6th_and_7th.jsp
More informationEach pair of opposite sides of a parallelogram is congruent to each other.
Find the perimeter and area of each parallelogram or triangle. Round to the nearest tenth if necessary. 1. Use the Pythagorean Theorem to find the height h, of the parallelogram. 2. Each pair of opposite
More informationCARMEL CLAY SCHOOLS MATHEMATICS CURRICULUM
GRADE 4 Standard 1 Number Sense Students understand the place value of whole numbers and decimals to two decimal places and how whole numbers 1 and decimals relate to simple fractions. 4.1.1 Read and write
More information128 Congruent and Similar Solids
Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar, state the scale factor. 3. Two similar cylinders have radii of 15 inches and 6 inches. What is the ratio
More informationShow that when a circle is inscribed inside a square the diameter of the circle is the same length as the side of the square.
Week & Day Week 6 Day 1 Concept/Skill Perimeter of a square when given the radius of an inscribed circle Standard 7.MG:2.1 Use formulas routinely for finding the perimeter and area of basic twodimensional
More informationPerimeter, Area, and Volume
Perimeter, Area, and Volume Perimeter of Common Geometric Figures The perimeter of a geometric figure is defined as the distance around the outside of the figure. Perimeter is calculated by adding all
More informationThe Area is the width times the height: Area = w h
Geometry Handout Rectangle and Square Area of a Rectangle and Square (square has all sides equal) The Area is the width times the height: Area = w h Example: A rectangle is 6 m wide and 3 m high; what
More informationName: Date: Geometry Solid Geometry. Name: Teacher: Pd:
Name: Date: Geometry 20122013 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 17 HW: Pgs: 810 DAY 2: SWBAT: Calculate the Volume of
More informationAlgebra Geometry Glossary. 90 angle
lgebra Geometry Glossary 1) acute angle an angle less than 90 acute angle 90 angle 2) acute triangle a triangle where all angles are less than 90 3) adjacent angles angles that share a common leg Example:
More informationChapter 7 Quiz. (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter?
Chapter Quiz Section.1 Area and Initial Postulates (1.) Which type of unit can be used to measure the area of a region centimeter, square centimeter, or cubic centimeter? (.) TRUE or FALSE: If two plane
More informationII. Geometry and Measurement
II. Geometry and Measurement The Praxis II Middle School Content Examination emphasizes your ability to apply mathematical procedures and algorithms to solve a variety of problems that span multiple mathematics
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 111: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationSolids. Objective A: Volume of a Solids
Solids Math00 Objective A: Volume of a Solids Geometric solids are figures in space. Five common geometric solids are the rectangular solid, the sphere, the cylinder, the cone and the pyramid. A rectangular
More informationStudy Guide. 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. Note: Figure is not drawn to scale.
Study Guide Name Test date 6.g.1 Find the area of triangles, quadrilaterals, and other polygons. 1. Note: Figure is not drawn to scale. If x = 14 units and h = 6 units, then what is the area of the triangle
More information(a) 5 square units. (b) 12 square units. (c) 5 3 square units. 3 square units. (d) 6. (e) 16 square units
1. Find the area of parallelogram ACD shown below if the measures of segments A, C, and DE are 6 units, 2 units, and 1 unit respectively and AED is a right angle. (a) 5 square units (b) 12 square units
More informationMAT 080Algebra II Applications of Quadratic Equations
MAT 080Algebra II Applications of Quadratic Equations Objectives a Applications involving rectangles b Applications involving right triangles a Applications involving rectangles One of the common applications
More informationMAT 0950 Course Objectives
MAT 0950 Course Objectives 5/15/20134/27/2009 A student should be able to R1. Do long division. R2. Divide by multiples of 10. R3. Use multiplication to check quotients. 1. Identify whole numbers. 2. Identify
More informationGrade 11 Essential Mathematics Unit 6: Measurement and Geometry
Grade 11 Essential Mathematics Unit 6: INTRODUCTION When people first began to take measurements, they would use parts of the hands and arms. For example, a digit was the width of a thumb. This kind of
More informationGeo  CH10 Practice Test
Geo  H10 Practice Test Multiple hoice Identify the choice that best completes the statement or answers the question. 1. lassify the figure. Name the vertices, edges, and base. a. triangular pyramid vertices:,,,,
More informationApplications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
More informationAdd and subtract 1digit and 2digit numbers to 20, including zero. Measure and begin to record length, mass, volume and time
Year 1 Maths  Key Objectives Count to and across 100 from any number Count, read and write numbers to 100 in numerals Read and write mathematical symbols: +,  and = Identify "one more" and "one less"
More informationascending order decimal denominator descending order Numbers listed from largest to smallest equivalent fraction greater than or equal to SOL 7.
SOL 7.1 ascending order Numbers listed in order from smallest to largest decimal The numbers in the base 10 number system, having one or more places to the right of a decimal point denominator The bottom
More information111. Space Figures and Cross Sections. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
111 Space Figures and Cross Sections Vocabulary Review Complete each statement with the correct word from the list. edge edges vertex vertices 1. A(n) 9 is a segment that is formed by the intersections
More informationMEASUREMENTS. U.S. CUSTOMARY SYSTEM OF MEASUREMENT LENGTH The standard U.S. Customary System units of length are inch, foot, yard, and mile.
MEASUREMENTS A measurement includes a number and a unit. 3 feet 7 minutes 12 gallons Standard units of measurement have been established to simplify trade and commerce. TIME Equivalences between units
More informationDescribe as a mixed number where the arrow is pointing to on the number line. Explain how the base 10 system relates to place value.
Number Properties and Operations Whole number sense and addition and subtraction are key concepts and skills developed in early childhood. Students build on their number sense and counting sense to develop
More information10.1: Areas of Parallelograms and Triangles
10.1: Areas of Parallelograms and Triangles Important Vocabulary: By the end of this lesson, you should be able to define these terms: Base of a Parallelogram, Altitude of a Parallelogram, Height of a
More informationLesson 4.2 Irrational Numbers Exercises (pages )
Lesson. Irrational Numbers Exercises (pages 11 1) A. a) 1 is irrational because 1 is not a perfect square. The decimal form of 1 neither terminates nor repeats. b) c) d) 16 is rational because 16 is a
More informationLESSON 10 GEOMETRY I: PERIMETER & AREA
LESSON 10 GEOMETRY I: PERIMETER & AREA INTRODUCTION Geometry is the study of shapes and space. In this lesson, we will focus on shapes and measures of onedimension and twodimensions. In the next lesson,
More informationPerimeter, Area, and Volume
Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the
More informationAn arrangement that shows objects in rows and columns Example:
1. acute angle : An angle that measures less than a right angle (90 ). 2. addend : Any of the numbers that are added 2 + 3 = 5 The addends are 2 and 3. 3. angle : A figure formed by two rays that meet
More informationPerimeter and Area. An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this.
UNIT 10 Perimeter and Area An artist uses perimeter and area to determine the amount of materials it takes to produce a piece such as this. 3 UNIT 10 PERIMETER AND AREA You can find geometric shapes in
More information*1. Understand the concept of a constant number like pi. Know the formula for the circumference and area of a circle.
Students: 1. Students deepen their understanding of measurement of plane and solid shapes and use this understanding to solve problems. *1. Understand the concept of a constant number like pi. Know the
More informationFourth Grade. Order the following numbers from smallest to largest: 576, 543, 562, A: 461.5, 543, 562, 576
Standard for Excellence: Number Sense Fourth Grade Mathematics Content Standard Performance Standard SAT 9 Number Sense 1.0 Students understand the place value of whole numbers and decimals to two decimal
More informationUnit 1, Review Transitioning from Previous Mathematics Instructional Resources: McDougal Littell: Course 1
Unit 1, Review Transitioning from Previous Mathematics Transitioning from previous mathematics to Sixth Grade Mathematics Understand the relationship between decimals, fractions and percents and demonstrate
More information7 th Grade Pre Algebra A Vocabulary Chronological List
SUM sum the answer to an addition problem Ex. 4 + 5 = 9 The sum is 9. DIFFERENCE difference the answer to a subtraction problem Ex. 8 2 = 6 The difference is 6. PRODUCT product the answer to a multiplication
More informationA. Areas of Parallelograms 1. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh.
Geometry  Areas of Parallelograms A. Areas of Parallelograms. If a parallelogram has an area of A square units, a base of b units, and a height of h units, then A = bh. A B Ex: See how VDFA V CGB so rectangle
More informationChapter 1 Measurement
Chapter 1 Measurement Math 1201 1 Chapter 1 Measurement Sections 1.11.3: Goals: Converting between imperial units by unit analysis Converting between SI units Converting between SI and imperial units
More informationPerimeter is the length of the boundary of a two dimensional figure.
Section 2.2: Perimeter and Area Perimeter is the length of the boundary of a two dimensional figure. The perimeter of a circle is called the circumference. The perimeter of any two dimensional figure whose
More informationGeometry Chapter 12. Volume. Surface Area. Similar shapes ratio area & volume
Geometry Chapter 12 Volume Surface Area Similar shapes ratio area & volume Date Due Section Topics Assignment Written Exercises 12.1 Prisms Altitude Lateral Faces/Edges Right vs. Oblique Cylinders 12.3
More informationWEIGHTS AND MEASURES. Linear Measure. 1 Foot12 inches. 1 Yard 3 feet  36 inches. 1 Rod 5 1/2 yards  16 1/2 feet
WEIGHTS AND MEASURES Linear Measure 1 Foot12 inches 1 Yard 3 feet  36 inches 1 Rod 5 1/2 yards  16 1/2 feet 1 Furlong 40 rods  220 yards  660 feet 1 Mile 8 furlongs  320 rods  1,760 yards 5,280 feet
More information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More information112 Areas of Trapezoids, Rhombi, and Kites. Find the area of each trapezoid, rhombus, or kite. 1. SOLUTION: 2. SOLUTION: 3.
Find the area of each trapezoid, rhombus, or kite. 1. 2. 3. esolutions Manual  Powered by Cognero Page 1 4. OPEN ENDED Suki is doing fashion design at 4H Club. Her first project is to make a simple Aline
More informationCalifornia Common Core State Standards Comparison FOURTH GRADE
1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others 4. Model with mathematics. Standards
More information