10.1 Areas of Quadrilaterals and triangles


 Charleen Sanders
 1 years ago
 Views:
Transcription
1 10.1 Areas of Quadrilaterals and triangles BASE AND HEIGHT MUST FORM A RIGHT ANGLE!! Draw the diagram, write the formula and SHOW YOUR WORK! FIND THE AREA OF THE FOLLOWING:. A rectangle with one side of length 1 mm and 1. A square with diagonal of length 1 m. The perimeter 40 mm. 3. A parallelogram with base 7 m and height 3 m. 4. A rectangle with diagonal of length 17 cm and base length of 15 cm. 5. An isosceles with base length 10 cm and 6. An equilateral with perimeter of 7 cm. 36 perimeter cm. 7. A parallelogram with sides 8 cm and 10 cm and an 8. A trapezoid with bases 13m and 1 m and height 5m. angle of A triangle with sides of lengths 8, 15,
2 All consecutive sides are perpendicular Find each missing measure The area of a triangle is 16 square units. If the height is 18 units, what is the length of the base? 15. The area of a trapezoid is 80 square units. If its height is 8 units, find the length of its median. (median = average of the bases) 16. The height of a trapezoid is 9 cm. The bases are 8 cm and 1 cm long. Find the area. 17. A trapezoid has an area of cm. If the altitude measure 3 cm and one base measures 36 cm, find the length of the other base. 18. The measure of the consecutive sides of an isosceles trapezoid are in the ratio 8:5::5. The perimeter of the trapezoid is 140 inches. If its height is 8 inches, find the area of the trapezoid A kite has diagonals of 5ft. and 11.3 ft. What is the area of the kite? 3. Find the area of a rhombus whose perimeter is 0 cm and whose diagonal is 8cm. 4. Find the area of a square with a diagonal of length 3.
3 10. Circle and Regular Polygons Regular Polygons: Apothem = Area = 7. Regular hexagon with side 8 cm. 3
4 Find the AREA of the figure. Draw diagram if needed. Show formula that you are using! 1. Square with a diagonal of 14 m.. Rectangle with length of 4 in. and diagonal of 5 in. 3. Parallelogram with sides 10 and 16 and a 30 angle. 4. An equilateral triangle with side of 15 yd. 5. Regular Hexagon with apothem of 3 cm. 6. Rhombus with diagonals of 14 and 1 meters. 7. An isosceles trapezoid with legs of 6 m. and bases of 10 m and 8 m. 8. Circle with circumference of Composite Figures 4
5 10.3 Composite Figures Find the shaded area. Round to the nearest tenth if necessary
6 10.5 SCALE FACTOR = Ratio of corresponding sides in similar polygons Scale Factor= ratio of heights/ ratio of radii/ ratio of bases/ ratio of diameters Are all triangles similar? Are all squares similar? All rectangles? All circles? Scale Factor: Ratio of Perimeters: a b a b a Ratio of Areas: b Ratio of Volume: a 3 b 3 Ex. 1 The ratio of the perimeters of similar triangles is 3: 4. Find the ratio of their areas. Ex. The ratio of the areas of circles is 16 : 49. Find the ratio of their diameters. Ex. 3 The perimeters of similar quadrilaterals are 48 and 60. The area of the smaller quadrilateral is 96 cm. Find the area of the larger quadrilateral. Ex. 4 The areas of similar triangles are 36 and 64. The length of a side of the smaller triangle is 1. Find the length of the corresponding side of the larger triangle. Describe the effect of each change on the area of the given figure. 1. The base of the parallelogram is multiplied by The length of a rectangle with length 1 yd and width 11 yd is divided by The base of a triangle with vertices A(, 3), B(5, ), and C(5, 4) is doubled. 4. The height of a trapezoid with base lengths 4 mm and 7 mm and height 9 mm is multiplied by 1 3. In Exercises 5 8, describe the effect of each change on the perimeter or circumference and the area of the given figure. 5. The length and width of the rectangle are multiplied by The base and height of a triangle with base 1.5 m and height 6 m are both tripled. 6
7 7. The radius of a circle with center (, ) that passes through (0, ) is divided by. 8. The bases and the height of a trapezoid with base lengths 4 in. and 8 in. and height 8 in. are all multiplied by A rhombus has an area of 9 cm. The area is multiplied by 5. Describe the effects on the diagonals of the rhombus. 10. A circle has a circumference of 14 ft. The area is halved. Describe the effects on the circumference of the circle. Find the similarity ratio for each pair of similar figures. 11. Two regular hexagons with areas 8 in. and 3 in. 1. Two squares with areas 81 cm and 5 cm 13. Two s with areas 10 ft and 360 ft 14. Two circles with areas 18π cm and 18 π cm. For each pair of similar figures, the area of the smaller figure is given. Find the area of the larger figure cm 7 in 5 in A = 18in A = 84 cm 1 in 5 in A = 0 in 15 cm 8 in For each pair of similar figures, find the ratio of the perimeters A = 7 cm A = 1 in A = 8 cm A = 1 cm A = 4 in A = 50 cm 19. The shorter sides of a rectangle are 6 ft. The shorter sides of a similar rectangle are 9 ft. The area of the smaller rectangle is 48 ft. What is the area of the larger rectangle? 7
8 10.6 Probability is the chance or likelihood that an event will occur. Probability = desired outcome total number of outcomes Ex. 1 There are 30 students in this class and 18 are male. If you choose a student from the class, what is the probability that you will pick a female student. (answer as a % ) Probability with lengths: desired length total length Ex. A point X is picked at random on AF. What is the probability that X is on: A B C D E F a) AC b) CE c) AF desired area Probability with Areas: 40 cm total area Use the square dart board for the following: The radius of the bull s eye is 4 cm. The radius of the middle circle is 8 cm. The radius of the largest circle is 1 cm. ROUND PERCENTS TO NEAREST TENTHS Ex. 3) Suppose you throw a dart onto the square dartboard, find the probability that the dart will land: a) in the bull s eye b) in the shaded area: 8
9 Ex 4. Find the probability that if a point is chosen inside the square, it will lie outside the circle. Ex. 5 Find the probability that if a point is inside the hexagon, it will lie in the shaded region. 11 in. 6 Ex. 6 Find the probability that if a tack is dropped in the rectangle, it will land a) in the circle b) outside of the circle Ex. 7 To win a carnival game, Max must throw a dart at a board four feet by three feet and hit one of the 5 circles on the board. The diameter of each circle is 4 inches. Approximately what percent of the time will a randomly thrown dart that hits the board also hit a circle? Ex. 8 A rectangle contains two inscribed semicircles and a full circle, as shown below. If a point is chosen at random inside the rectangle, what is the approximate probability that the point will also be in the shaded region? Thee dart board shown has 5 concentric circles whose centers are also the center of the square board. Each side of the board is 38 cm, and the radii of the circles are cm, 5 cm, 8 cm, 11 cm, and 14 cm. A dart hitting within one of the circular regions scores the number of points indicated on the board, while a hit anywhere else scores 0 points. If a dart, thrown at random, hits the board, find the probability of scoring the indicated number of points points 8. 1 point 9. points points points 1. 5 points Find the probability that a point chosen at random from AK is on the given segment. A B C D E F G H I J K CF 5. BI 6. GK 7. FG 8. AK 5 9. AC
10 11. That state of Connecticut is approximated by a rectangle 100 mi by 50 mi. Hartford is approximately at the center of the state. If a meteor hit earth within 00 mi of Hartford, find the probability that the meteor landed in Connecticut. 1. A stop light at an intersection stays red for 60 second, changes to green for 45 seconds, and then yellow for 15 seconds. If Joel arrives at the intersection at a random time, what is the probability that he will have to wait at a red light for more than 15 seconds? Find the area of the following: All consecutive sides are Area= 6 15 scale factor: 3 Circum.= ratio of perimeters: Area: Ratio of areas: 10. Find the base of a rectangle with height 7 cm and area 91 cm. 1. Find the area of a rhombus whose diagonals are 8 cm and 1 cm long. 13. Find the height of a trapezoid with longer base 30 cm, shorter base 1 cm, and area 105 cm. 14. Find the area of a regular hexagon whose radius is 4 in. 15. Find the area of an equilateral whose side is 8 mm. 16. If octagons are similar with a scale factor of 4:7, find the ratio of their areas. 17. Isosceles trapezoid ABCD has bases AB = 37 and CD = 13. If XD = 17, the area of XYCD is what % of the area of ABCD? 18. The area of parallelogram with bases of 6 cm and 1cm and one angle of 30 is? B C 19. The area of a circle is 75. Find the Circumference in terms of. 1. A triangle has a hypotenuse of length 3 cm. What is the area of the triangle? 10 A D
11 . An isosceles right triangle has a hypotenuse with length 10. What is the area of the right triangle? 3. In the diagram, rhombus ABCD has area 16 m and BD = 18m. Find CA. 4. In the diagram, the perimeter of EFGH is 50 mm. If EF = 1 mm, what is the area of the rectangle? 5. A triangle has an area of 50 units. What is the length of the hypotenuse? 6. What is the area of a parallelogram with a 45 degree angle and sides of length 6 cm and 7 cm? E 7. In the diagram, parallelogram TRAC has TR = 1, RA = 14, and RK = 10. What is the area of the parallelogram? H F G 8. A trapezoid has an area of 33 cm. Find the longer base if the shorter base is 4cm and the height is 6 cm. 9. In the diagram, ABCDE is a regular pentagon with side lengths 6m. OX = 4.13 m. Find the area to the nearest tenth of a meter. 10. What is the area of a regular triangle with a radius of 8 units? A B O C R A 13. A regular hexagon has a side of length 8 cm. Find the area of the hexagon. E X 14. Two regular pentagons have sides of 14m and 3.5 m, respectively. Find their scale factor, ratio of their perimeters and areas. 15. Two regular octagons have perimeters 16 cm and 3cm, respectively. Find the scale factor and the ratio of their areas. 16. Two similar polygons have a scale factor 7 : 5. The area of the larger polygon is 147 u. Find the area of the smaller polygon. 17. The areas of circles are 100 and 36. Find the ratio of their radii and their circumferences. 18. The circumference of a circle is 6. Find its area. D T K C 11
12 Chapter 10 Area of D Shapes Tuesday 4/5 Thursday 4/7 Monday 4/11 Wednesday 4/13 Friday 4/15 Tuesday 4/19 Thursday 4/1 Monday 4/ and 10. Areas of Triangles and Quadrilaterals, Circles, and Regular Polygons Packet Pages 14 Keys Trip 10.1 and 10. Review Packet Pages 14 Keys Trip More Review 10.3 Composite Figures Review Packet Pages 5 QUIZ # Ratios of Similar Figures Packet Pages Geometric Probability Packet Pages 810 QUIZ # Review Packet Pages Unit 10 Test HW: HW and Packet Pages 14 are due on Wednesday 4/13 Yackey not in class HW and Packet Pages 14 are due on Wednesday 4/13 Yackey not in class HW and Packet Pages 14 are due on Wednesday 4/13 HW: HW: HW: HW: Finish Packet TURN IN PACKET AT BEGINNING OF CLASS HW: None :) Area of a square: s Perimeter of a square: 4s Area of a Rectangle: bh Perimeter of a Rectangle: b + h or (l + w) bh 1 Area of a Triangle: or bh Area of a Parallelogram: bh d1 d Area of a Rhombus or Kite: b 1 b h Area of a Trapezoid: Area of a Circle: r Area of s Equilateral : or d1 d 1 h b1 b Circumference of a Circle: r or d or measure of arc a Sector : r 360 1
A. 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 informationPerimeter and area formulas for common geometric figures:
Lesson 10.1 10.: Perimeter and Area of Common Geometric Figures Focused Learning Target: I will be able to Solve problems involving perimeter and area of common geometric figures. Compute areas of rectangles,
More informationCircumference Pi Regular polygon. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GPreAP UNIT 14: PERIMETER AND AREA I can define, identify and illustrate the following terms: Perimeter Area Base Height Diameter Radius Circumference Pi Regular polygon Apothem Composite
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 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 informationArea. Area Overview. Define: Area:
Define: Area: Area Overview Kite: Parallelogram: Rectangle: Rhombus: Square: Trapezoid: Postulates/Theorems: Every closed region has an area. If closed figures are congruent, then their areas are equal.
More informationGeometry Chapter 9 Extending Perimeter, Circumference, and Area
Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Targets LT91: Solve problems involving the perimeter and area of
More informationGeometry Chapter 9 Extending Perimeter, Circumference, and Area
Geometry Chapter 9 Extending Perimeter, Circumference, and Area Lesson 1 Developing Formulas for Triangles and Quadrilaterals Learning Target (LT1) Solve problems involving the perimeter and area of triangles
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 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 informationChapter 11. Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem!
Chapter 11 Areas of Plane Figures You MUST draw diagrams and show formulas for every applicable homework problem! Objectives A. Use the terms defined in the chapter correctly. B. Properly use and interpret
More informationUnit 7 Syllabus: Area
Date Period Day Topic Unit 7 Syllabus: Area 1 Areas of Parallelograms and Triangles 2 Areas of Trapezoids, Rhombuses and Kites 3 Areas of Regular Polygons 4 Quiz 5 Perimeters and Areas of Similar Figures
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 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 information3. If AC = 12, CD = 9 and BE = 3, find the area of trapezoid BCDE. (Mathcounts Handbooks)
EXERCISES: Triangles 1 1. The perimeter of an equilateral triangle is units. How many units are in the length 27 of one side? (Mathcounts Competitions) 2. In the figure shown, AC = 4, CE = 5, DE = 3, and
More information114 Areas of Regular Polygons and Composite Figures
1. In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. Center: point F, radius:, apothem:,
More information10.1 Geometry Areas of Parallelograms, Triangles and Heron s Formula
Name Due Date 4/10 https://www.youtube.com/watch?v=eh5zawhrioo 10.1 Geometry Areas of Parallelograms, Triangles and Heron s Formula Area of a Rectangle: A= Area of a Square: A= Area of a Parallelogram:
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 informationThe area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2
The area of a figure is the measure of the size of the region enclosed by the figure. Formulas for the area of common figures: square: A = s 2 s s rectangle: A = l w parallelogram: A = b h h b triangle:
More informationLEVEL G, SKILL 1. Answers Be sure to show all work.. Leave answers in terms of ϖ where applicable.
Name LEVEL G, SKILL 1 Class Be sure to show all work.. Leave answers in terms of ϖ where applicable. 1. What is the area of a triangle with a base of 4 cm and a height of 6 cm? 2. What is the sum of the
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 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 informationWorking in 2 & 3 dimensions Revision Guide
Tips for Revising Working in 2 & 3 dimensions Make sure you know what you will be tested on. The main topics are listed below. The examples show you what to do. List the topics and plan a revision timetable.
More information2006 Geometry Form A Page 1
2006 Geometry Form Page 1 1. he hypotenuse of a right triangle is 12" long, and one of the acute angles measures 30 degrees. he length of the shorter leg must be: () 4 3 inches () 6 3 inches () 5 inches
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 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 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 informationSA B 1 p where is the slant height of the pyramid. V 1 3 Bh. 3D Solids Pyramids and Cones. Surface Area and Volume of a Pyramid
Accelerated AAG 3D Solids Pyramids and Cones Name & Date Surface Area and Volume of a Pyramid The surface area of a regular pyramid is given by the formula SA B 1 p where is the slant height of the pyramid.
More informationCSU Fresno Problem Solving Session. Geometry, 17 March 2012
CSU Fresno Problem Solving Session Problem Solving Sessions website: http://zimmer.csufresno.edu/ mnogin/mfdprep.html Math Field Day date: Saturday, April 21, 2012 Math Field Day website: http://www.csufresno.edu/math/news
More informationChapter 11 Resource Masters
Chapter 11 Resource Masters 111 Study Guide and Intervention Areas of Parallelograms and Triangles Areas of Parallelograms Any side of a parallelogram can be called a base. The height of a parallelogram
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 informationGeometry Honors: Extending 2 Dimensions into 3 Dimensions. Unit Overview. Student Focus. Semester 2, Unit 5: Activity 30. Resources: Online Resources:
Geometry Honors: Extending 2 Dimensions into 3 Dimensions Semester 2, Unit 5: Activity 30 Resources: SpringBoard Geometry Online Resources: Geometry Springboard Text Unit Overview In this unit students
More informationTopics Covered on Geometry Placement Exam
Topics Covered on Geometry Placement Exam  Use segments and congruence  Use midpoint and distance formulas  Measure and classify angles  Describe angle pair relationships  Use parallel lines and transversals
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Wednesday, August 18, 2010 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of
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 informationHonors Geometry Final Exam Study Guide
20112012 Honors Geometry Final Exam Study Guide Multiple Choice Identify the choice that best completes the statement or answers the question. 1. In each pair of triangles, parts are congruent as marked.
More informationUpper Elementary Geometry
Upper Elementary Geometry Geometry Task Cards Answer Key The unlicensed photocopying, reproduction, display, or projection of the material, contained or accompanying this publication, is expressly prohibited
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 informationConjectures. Chapter 2. Chapter 3
Conjectures Chapter 2 C1 Linear Pair Conjecture If two angles form a linear pair, then the measures of the angles add up to 180. (Lesson 2.5) C2 Vertical Angles Conjecture If two angles are vertical
More information2nd Semester Geometry Final Exam Review
Class: Date: 2nd Semester Geometry Final Exam Review Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The owner of an amusement park created a circular
More informationPERIMETERS AND AREAS
PERIMETERS AND AREAS 1. PERIMETER OF POLYGONS The Perimeter of a polygon is the distance around the outside of the polygon. It is the sum of the lengths of all the sides. Examples: The perimeter of this
More information133 Geometric Probability. 1. P(X is on ) SOLUTION: 2. P(X is on ) SOLUTION:
Point X is chosen at random on. Find the probability of each event. 1. P(X is on ) 2. P(X is on ) 3. CARDS In a game of cards, 43 cards are used, including one joker. Four players are each dealt 10 cards
More information28. [Area / Volume] cm 2. in = =
8. [ / Volume] Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). Count the number of fully shaded squares on the grid. If necessary add on the number of half
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 information1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area?
1. A person has 78 feet of fencing to make a rectangular garden. What dimensions will use all the fencing with the greatest area? (a) 20 ft x 19 ft (b) 21 ft x 18 ft (c) 22 ft x 17 ft 2. Which conditional
More informationGAP CLOSING. 2D Measurement. Intermediate / Senior Student Book
GAP CLOSING 2D Measurement Intermediate / Senior Student Book 2D Measurement Diagnostic...3 Areas of Parallelograms, Triangles, and Trapezoids...6 Areas of Composite Shapes...14 Circumferences and Areas
More informationSigns, Signs, Every Place There Are Signs! Area of Regular Polygons p. 171 Boundary Lines Area of Parallelograms and Triangles p.
C H A P T E R Perimeter and Area Regatta is another word for boat race. In sailing regattas, sailboats compete on courses defined by marks or buoys. These courses often start and end at the same mark,
More informationSpecial case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2
Geometry Chapter 11/12 Review Shape: Rectangle Formula A= Base x Height Special case: Square. The same formula works, but you can also use A= Side x Side or A= (Side) 2 Height = 6 Base = 8 Area = 8 x 6
More informationCONJECTURES  Discovering Geometry. Chapter 2
CONJECTURES  Discovering Geometry Chapter C1 Linear Pair Conjecture  If two angles form a linear pair, then the measures of the angles add up to 180. C Vertical Angles Conjecture  If two angles are
More informationBASIC GEOMETRY GLOSSARY
BASIC GEOMETRY GLOSSARY Acute angle An angle that measures between 0 and 90. Examples: Acute triangle A triangle in which each angle is an acute angle. Adjacent angles Two angles next to each other that
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 informationChapter 8 Geometry We will discuss following concepts in this chapter.
Mat College Mathematics Updated on Nov 5, 009 Chapter 8 Geometry We will discuss following concepts in this chapter. Two Dimensional Geometry: Straight lines (parallel and perpendicular), Rays, Angles
More information101. Areas of Parallelograms and Triangles. Vocabulary. Review. Vocabulary Builder. Use Your Vocabulary
 Areas of Parallelograms and Triangles Vocabulary Review The diagram below shows the different types of parallelograms. Parallelogram Rhombus Rectangle Square Underline the correct word to complete each
More informationConjectures for Geometry for Math 70 By I. L. Tse
Conjectures for Geometry for Math 70 By I. L. Tse Chapter Conjectures 1. Linear Pair Conjecture: If two angles form a linear pair, then the measure of the angles add up to 180. Vertical Angle Conjecture:
More informationFS Geometry EOC Review
MAFS.912.GC.1.1 Dilation of a Line: Center on the Line In the figure, points A, B, and C are collinear. http://www.cpalms.org/public/previewresource/preview/72776 1. Graph the images of points A, B, and
More information2006 ACTM STATE GEOMETRY EXAM
2006 TM STT GOMTRY XM In each of the following you are to choose the best (most correct) answer and mark the corresponding letter on the answer sheet provided. The figures are not necessarily drawn to
More informationare radii of the same circle. So, they are equal in length. Therefore, DN = 8 cm.
For Exercises 1 4, refer to. 1. Name the circle. The center of the circle is N. So, the circle is 2. Identify each. a. a chord b. a diameter c. a radius a. A chord is a segment with endpoints on the circle.
More informationGEOMETRY FINAL EXAM REVIEW
GEOMETRY FINL EXM REVIEW I. MTHING reflexive. a(b + c) = ab + ac transitive. If a = b & b = c, then a = c. symmetric. If lies between and, then + =. substitution. If a = b, then b = a. distributive E.
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 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 informationSum of the interior angles of a nsided Polygon = (n2) 180
5.1 Interior angles of a polygon Sides 3 4 5 6 n Number of Triangles 1 Sum of interiorangles 180 Sum of the interior angles of a nsided Polygon = (n2) 180 What you need to know: How to use the formula
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 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 information1 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
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
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 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 informationFinal Review Problems Geometry AC Name
Final Review Problems Geometry Name SI GEOMETRY N TRINGLES 1. The measure of the angles of a triangle are x, 2x+6 and 3x6. Find the measure of the angles. State the theorem(s) that support your equation.
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 information2 feet Opposite sides of a rectangle are equal. All sides of a square are equal. 2 X 3 = 6 meters = 18 meters
GEOMETRY Vocabulary 1. Adjacent: Next to each other. Side by side. 2. Angle: A figure formed by two straight line sides that have a common end point. A. Acute angle: Angle that is less than 90 degree.
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 informationUnit 3: Triangle Bisectors and Quadrilaterals
Unit 3: Triangle Bisectors and Quadrilaterals Unit Objectives Identify triangle bisectors Compare measurements of a triangle Utilize the triangle inequality theorem Classify Polygons Apply the properties
More informationGEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT!
GEOMETRY 101* EVERYTHING YOU NEED TO KNOW ABOUT GEOMETRY TO PASS THE GHSGT! FINDING THE DISTANCE BETWEEN TWO POINTS DISTANCE FORMULA (x₂x₁)²+(y₂y₁)² Find the distance between the points ( 3,2) and
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 information0810ge. Geometry Regents Exam 0810
0810ge 1 In the diagram below, ABC XYZ. 3 In the diagram below, the vertices of DEF are the midpoints of the sides of equilateral triangle ABC, and the perimeter of ABC is 36 cm. Which two statements identify
More informationGeometry SOL G.11 G.12 Circles Study Guide
Geometry SOL G.11 G.1 Circles Study Guide Name Date Block Circles Review and Study Guide Things to Know Use your notes, homework, checkpoint, and other materials as well as flashcards at quizlet.com (http://quizlet.com/4776937/chapter10circlesflashcardsflashcards/).
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 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 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 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 information104 Inscribed Angles. Find each measure. 1.
Find each measure. 1. 3. 2. intercepted arc. 30 Here, is a semicircle. So, intercepted arc. So, 66 4. SCIENCE The diagram shows how light bends in a raindrop to make the colors of the rainbow. If, what
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 informationTarget To know the properties of a rectangle
Target To know the properties of a rectangle (1) A rectangle is a 3D shape. (2) A rectangle is the same as an oblong. (3) A rectangle is a quadrilateral. (4) Rectangles have four equal sides. (5) Rectangles
More informationHonors Packet on. Polygons, Quadrilaterals, and Special Parallelograms
Honors Packet on Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: #1 6 in packet HW: Pages 386
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 informationDate: Period: Symmetry
Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into
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 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 informationGeometry Unit 6 Areas and Perimeters
Geometry Unit 6 Areas and Perimeters Name Lesson 8.1: Areas of Rectangle (and Square) and Parallelograms How do we measure areas? Area is measured in square units. The type of the square unit you choose
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 informationCHAPTER 6. Polygons, Quadrilaterals, and Special Parallelograms
CHAPTER 6 Polygons, Quadrilaterals, and Special Parallelograms Table of Contents DAY 1: (Ch. 61) SWBAT: Find measures of interior and exterior angles of polygons Pgs: 17 HW: Pgs: 810 DAY 2: (62) Pgs:
More information1) Find perimeter and area of the figure. 2) Find perimeter and area of the figure.
WS#1: PERIMETER AND AREA (H) NAME PD 1) Find perimeter and area of the figure. 2) Find perimeter and area of the figure. For the following exercises, use the figure and measurements below to find the indicated
More informationMath Tech 1 Unit 11. Perimeter, Circumference and Area. Name Pd
Math Tech 1 Unit 11 Perimeter, Circumference and Area Name Pd 111 Perimeter Perimeter  Units  Ex. 1: Find the perimeter of a rectangle with length 7 m and width 5 m. Ex. 2: Find the perimeter of the
More informationA. 3y = 2x + 1. y = x + 3. y = x  3. D. 2y = 3x + 3
Name: Geometry Regents Prep Spring 2010 Assignment 1. Which is an equation of the line that passes through the point (1, 4) and has a slope of 3? A. y = 3x + 4 B. y = x + 4 C. y = 3x  1 D. y = 3x + 1
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Thursday, August 13, 2009 8:30 to 11:30 a.m., only.
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, August 13, 2009 8:30 to 11:30 a.m., only Student Name: School Name: Print your name and the name of your
More information114 Areas of Regular Polygons and Composite Figures
1.In the figure, square ABDC is inscribed in F. Identify the center, a radius, an apothem, and a central angle of the polygon. Then find the measure of a central angle. SOLUTION: Center: point F, radius:,
More informationThe University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY. Student Name:
GEOMETRY The University of the State of New York REGENTS HIGH SCHOOL EXAMINATION GEOMETRY Thursday, June 17, 2010 1:15 to 4:15 p.m., only Student Name: School Name: Print your name and the name of your
More informationGEOMETRY EXAMINATION
First Round: February 8, 015 at Regional Testing Centers Second Round: April 11, 015 at University of North Alabama GEOMETRY EXAMINATION Construction of this test directed by Scott H. Brown and Luke Smith,
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 information, where B is the area of the base and h is the height of the pyramid. The base
Find the volume of each pyramid. The volume of a pyramid is, where B is the area of the base and h is the height of the pyramid. The base of this pyramid is a right triangle with legs of 9 inches and 5
More informationIdentifying Triangles 5.5
Identifying Triangles 5.5 Name Date Directions: Identify the name of each triangle below. If the triangle has more than one name, use all names. 1. 5. 2. 6. 3. 7. 4. 8. 47 Answer Key Pages 19 and 20 Name
More information