Basic Math for the Small Public Water Systems Operator


 Shanna Posy Price
 3 years ago
 Views:
Transcription
1 Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg
2 Introduction Area In this module we will learn how to calculate the area of some basic shapes that include the: Rectangle, Triangle, and Circle
3 Overview Calculating the area of a basic shape is a necessary step in determining the volume or capacity of a container. Being able to calculate the surface area of a tank has practical applications as well. For example, knowing the surface area of a tank will enable you to estimate the quantity of paint required to paint that tank.
4 Basic Shapes Rectangle Triangle Circle Cylinder
5 Area Calculations Area calculations are two dimensional. They involve two dimensions such as length and width. For example when we multiply the linear unit feet times the linear unit feet we get the area unit measurement of square feet.
6 Area Calculations So the unit multiplication ft x ft gives the 2 answer ft or sq ft. An example in the Metric system of measurement would be to multiply the linear unit meter times the linear unit meter 2 for a result of m or sq m.
7 Calculating the Area of a Rectangle The formula to calculate the area of a rectangle is: Area = (Length)(Width) or A = (L)(W) Width Length
8 Example  Calculating the Area of a Rectangle Calculate the area of a rectangle whose length is 25 feet and whose width is 15 feet. Area = Length (Feet) x Width (Feet) Area = 25 ft x 15 ft Area = 375 sq ft 15 ft 25 ft
9 Practice Exercise 1. Calculate the area of a rectangle whose length is 50 feet and whose width is 30 feet. 50 ft 30 ft Answer: 1,500 sq ft
10 Solution: 50 ft 30 ft Area = Length (Feet) x Width (Feet) Area = 50 ft x 30 ft Area = 1,500 ft 2
11 Practice Exercise 2. Calculate the area of a rectangle whose length is 42 feet and whose width is 23 feet. 42 ft 23 ft Answer: 966 sq ft
12 Solution: 42 ft 23 ft Area = Length (Feet) x Width (Feet) Area = 42 ft x 23 ft Area = 966 ft 2
13 Height Calculating the Area of a Triangle The formula to calculate the area of a triangle is: Base Area = (Base)(Height) 2 or A = (B)(H) 2
14 Example Calculating the Area of a Triangle Calculate the area of a triangle whose base is 16 feet and whose height is 32 feet. Area (Square Feet) = Base (Feet) x Height (Feet) 2 Area = 16 ft x 32 ft 2 32 ft Area = 256 sq ft 16 ft
15 Practice Exercise 1. Calculate the area of a triangle whose base is 60 feet and whose height is 120 feet. 60 ft 120 ft Answer: 3,600 sq ft
16 Solution: Area = (Base)(Height) 2 Area = 60 ft x 120 ft 2 Area = 3,600 ft 2 60 ft 120 ft
17 Practice Exercise 2. Calculate the area of a triangle whose base is 54 feet and whose height is 152 feet. 54 ft 152 ft Answer: 4,104 sq ft
18 Solution: Area = (Base)(Height) 2 Area = 54 ft x 152 ft 2 Area = 4,104 ft 2 54 ft 152 ft
19 Calculating the Circumference of a Circle The circumference of a circle is the distance around the circle. The formula to calculate the circumference of Diameter C = x D Where (pronounced pi) is the Greek symbol for the value 3.14 and D is the diameter.
20 Example Calculating the Circumference of a Circle Calculate the circumference of a circle whose diameter is 3 feet. D = 3 ft Circumference = 3.14 x 3 ft Circumference = 9.42 ft
21 Practice Exercise 1. Calculate the circumference of a circle whose diameter is 5 feet. 5 ft Answer: 15.7 ft
22 Solution: Circumference = x D C = x 5 ft C = 3.14 x 5 ft C = 15.7 ft 5 ft
23 Practice Exercise 2. Calculate the circumference of a circle whose diameter is 25 feet. 25 ft Answer: 78.5 ft
24 Solution: C = x D C = x 25 ft C = 3.14 x 25 ft C = 78.5 ft 25 ft
25 Calculating the Area of a Circle The formula to calculate the area of a circle is: Diameter Area = x r Where (pronounced pi) is the Greek symbol for the value 3.14 and r is the radius squared. 2
26 Relationship of the Radius to the Diameter of a Circle The diameter of a circle is two times the radius. Diameter Diameter = 2 x Radius or D = 2 x r
27 Example Calculating the Area of a Circle Calculate the area of a circle whose radius is 4 feet. r 4 ft Area = x r 2 Area = 3.14 x (4 ft) 2 Area = 3.14 x 16 sq ft Area = sq ft
28 Practice Exercise 1. Calculate the area of a circle whose radius is 5 feet. r 5 ft Answer: 78.5 sq ft
29 Solution: Area = x r 2 Area = 3.14 x (5 ft) 2 Area = 78.5 ft 2 r 5 ft
30 Practice Exercise 2. Calculate the area of a circle whose diameter is 50 feet. Hint: The diameter divided in half is equal to the radius. Answer: 1,963.5 sq ft 50 ft
31 Solution: Area = x r 2 Area = 3.14 x (25 ft) 2 50 ft Area =1,963.5 ft 2
32 Calculating the Surface Area of a Cylinder To calculate the surface area break the cylinder down into its component parts. That is two circles and its wall. Circumference = x Diameter Height
33 Surface Area of a Cylinder We already know how to calculate the area of a circle by applying the formula: Area = x r 2 Remember the cylinder is comprised of two circles, therefore it is necessary to multiply the above formula by 2.
34 Surface Area of a Cylinder To calculate the area of the cylinder wall, first calculate its length by using the following formula: Area = x D Where D is the diameter of the circle. Next multiply this result by the height of the tank.
35 Surface Area of a Cylinder Finally, add the area of the two circles and the area of the tank wall to obtain the total surface area of the tank.
36 Example Calculating the Surface Area of a Cylinder Calculate the surface area of a tank with a radius of 35 feet and a height of 45 feet. First: Calculate the area of the tank top and bottom as follows: Area = 2 x x r 2 Area = 2 x 3.14 x (35 ft) 2 Area = 7,693 sq ft
37 Example Calculating the Surface Area of a Cylinder Next: Calculate the length of the tank wall as follows: Length = x D Length = 3.14 x 70 ft Length = 220 ft Remember, the diameter is found by multiplying the radius by 2.
38 Example Calculating the Surface Area of a Cylinder Next: Multiply the length of the tank wall by the height of the tank to obtain the area of the tank wall: Area = Length x Height Area = 220 ft x 45 ft Area = 9,900 sq ft
39 Example Calculating the Surface Area of a Cylinder Finally, add the area of the tank top and bottom together with the area of the tank wall to obtain the total surface area of the tank. 7,693 sq ft + 9,900 sq ft = 17,593 sq ft
40 Practice Exercise 1. Calculate the surface area of a tank with a diameter of 20 feet and a height of 40 feet. 20 ft 40 ft Answer: 3,140 sq ft
41 Solution: Area of tank top and bottom: 2 x x r 2 2 x 3.14 x (10 ft) 2 = 628 ft 2 Length of tank wall: x Diameter x 20 ft = 62.8 ft 20 ft 40 ft
42 Solution Continued 20 ft Area of tank wall: Length x Height 62.8 ft x 40 ft = 2,512 ft 2 Total area of tank: 628 ft 2 + 2,512 ft 2 = 3,140 ft 2 40 ft
43 Practice Exercise 2. Calculate the surface area of a tank with a diameter of 15 feet and a height of 20 feet. 15 ft 20 ft Answer: 1, sq ft
44 Solution: Area of tank top and bottom: 2 x x r 2 2 x 3.14 x (7.5 ft) 2 = ft 2 Length of tank wall: x Diameter x 15 ft = 47.1 ft 15 ft 20 ft
45 Solution Continued Area of tank wall: Length x Height 47.1 ft x 20 ft = 942 ft 2 Total area of tank: ft ft 2 = 1, ft 2 15 ft 20 ft
46 Summary At the completion of this training module you should be able to calculate the area of the three basic shapes introduced; the rectangle, triangle and the circle. The next module demonstrates how to expand upon area calculations to determine volumes of various types of tanks, which are components of our water treatment systems.
Area 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 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 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 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 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 informationCalculating the surface area of a threedimensional object is similar to finding the area of a two dimensional object.
Calculating the surface area of a threedimensional object is similar to finding the area of a two dimensional object. Surface area is the sum of areas of all the faces or sides of a threedimensional
More informationIn Problems #1  #4, find the surface area and volume of each prism.
Geometry Unit Seven: Surface Area & Volume, Practice In Problems #1  #4, find the surface area and volume of each prism. 1. CUBE. RECTANGULAR PRISM 9 cm 5 mm 11 mm mm 9 cm 9 cm. TRIANGULAR PRISM 4. TRIANGULAR
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 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 informationArea of a triangle: The area of a triangle can be found with the following formula: 1. 2. 3. 12in
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 Solve: Find the area of each triangle. 1. 2. 3. 5in4in 11in 12in 9in 21in 14in 19in 13in
More informationSection 7.2 Area. The Area of Rectangles and Triangles
Section 7. Area The Area of Rectangles and Triangles We encounter two dimensional objects all the time. We see objects that take on the shapes similar to squares, rectangle, trapezoids, triangles, and
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 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 informationGrade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area. Determine the area of various shapes Circumference
1 P a g e Grade 9 Mathematics Unit 3: Shape and Space Sub Unit #1: Surface Area Lesson Topic I Can 1 Area, Perimeter, and Determine the area of various shapes Circumference Determine the perimeter of various
More informationFinding Volume of Rectangular Prisms
MA.FL.7.G.2.1 Justify and apply formulas for surface area and volume of pyramids, prisms, cylinders, and cones. MA.7.G.2.2 Use formulas to find surface areas and volume of threedimensional composite shapes.
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 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 informationAREA. AREA is the amount of surface inside a flat shape. (flat means 2 dimensional)
AREA AREA is the amount of surface inside a flat shape. (flat means 2 dimensional) Area is always measured in units 2 The most basic questions that you will see will involve calculating the area of a square
More informationSurface Area Quick Review: CH 5
I hope you had an exceptional Christmas Break.. Now it's time to learn some more math!! :) Surface Area Quick Review: CH 5 Find the surface area of each of these shapes: 8 cm 12 cm 4cm 11 cm 7 cm Find
More informationPerimeter. 14ft. 5ft. 11ft.
Perimeter The perimeter of a geometric figure is the distance around the figure. The perimeter could be thought of as walking around the figure while keeping track of the distance traveled. To determine
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 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 informationYOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!
DETAILED SOLUTIONS AND CONCEPTS  SIMPLE GEOMETRIC FIGURES Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST
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 informationGeometry Notes VOLUME AND SURFACE AREA
Volume and Surface Area Page 1 of 19 VOLUME AND SURFACE AREA Objectives: After completing this section, you should be able to do the following: Calculate the volume of given geometric figures. Calculate
More informationPizza! Pizza! Assessment
Pizza! Pizza! Assessment 1. A local pizza restaurant sends pizzas to the high school twelve to a carton. If the pizzas are one inch thick, what is the volume of the cylindrical shipping carton for the
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 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 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 informationSurface Area of Prisms
Surface Area of Prisms Find the Surface Area for each prism. Show all of your work. Surface Area: The sum of the areas of all the surface (faces) if the threedimensional figure. Rectangular Prism: A prism
More informationSection 2.4: Applications and Writing Functions
CHAPTER 2 Polynomial and Rational Functions Section 2.4: Applications and Writing Functions Setting up Functions to Solve Applied Problems Maximum or Minimum Value of a Quadratic Function Setting up Functions
More informationCalculating the Surface Area of a Cylinder
Calculating the Measurement Calculating The Surface Area of a Cylinder PRESENTED BY CANADA GOOSE Mathematics, Grade 8 Introduction Welcome to today s topic Parts of Presentation, questions, Q&A Housekeeping
More informationCONNECT: Areas, Perimeters
CONNECT: Areas, Perimeters 1. AREAS OF PLANE SHAPES A plane figure or shape is a twodimensional, flat shape. Here are 3 plane shapes: All of them have two dimensions that we usually call length and width
More informationThe GED math test gives you a page of math formulas that
Math Smart 643 The GED Math Formulas The GED math test gives you a page of math formulas that you can use on the test, but just seeing the formulas doesn t do you any good. The important thing is understanding
More informationGeometry  Calculating Area and Perimeter
Geometry  Calculating Area and Perimeter In order to complete any of mechanical trades assessments, you will need to memorize certain formulas. These are listed below: (The formulas for circle geometry
More informationGrade 4 Mathematics Measurement: Lesson 2
Grade 4 Mathematics Measurement: Lesson 2 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
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 informationModule: Fundamental Construction Math
Module: Fundamental Construction Math Overview: A background review of fundamental math principles, concepts, and calculation used in common construction activities including estimating, load calculations,
More informationTopic 9: Surface Area
Topic 9: Surface Area for use after Covering and Surrounding (Investigation 5) Jillian is wrapping a box of model cars for her brother s birthday. Jillian needs to measure the box to see if she has enough
More informationFunctional Skills Mathematics
Functional Skills Mathematics Level Learning Resource Perimeter and Area MSS1/L.7 Contents Perimeter and Circumference MSS1/L.7 Pages 36 Finding the Area of Regular Shapes MSS1/L.7 Page 710 Finding the
More information17.2 Surface Area of Prisms and Cylinders
Name Class Date 17. Surface Area of Prisms and Cylinders Essential Question: How can you find the surface area of a prism or cylinder? Explore G.11.C Apply the formulas for the total and lateral surface
More information1. Kyle stacks 30 sheets of paper as shown to the right. Each sheet weighs about 5 g. How can you find the weight of the whole stack?
Prisms and Cylinders Answer Key Vocabulary: cylinder, height (of a cylinder or prism), prism, volume Prior Knowledge Questions (Do these BEFORE using the Gizmo.) [Note: The purpose of these questions is
More informationSURFACE AREA AND VOLUME
SURFACE AREA AND VOLUME In this unit, we will learn to find the surface area and volume of the following threedimensional solids:. Prisms. Pyramids 3. Cylinders 4. Cones It is assumed that the reader has
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 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 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 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 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, Circumference, Area and Ratio LongTerm Memory Review
Review 1 1. Which procedure is used to find the perimeter of any polygon? A) Add all the lengths B) Multiply length times width ( l w ) C) Add only one length and one width D) Multiply all of the lengths
More information104 Surface Area of Prisms and Cylinders
: Finding Lateral Areas and Surface Areas of Prisms 2. Find the lateral area and surface area of the right rectangular prism. : Finding Lateral Areas and Surface Areas of Right Cylinders 3. Find the lateral
More informationGrade 8 Mathematics Measurement: Lesson 6
Grade 8 Mathematics Measurement: Lesson 6 Read aloud to the students the material that is printed in boldface type inside the boxes. Information in regular type inside the boxes and all information outside
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 informationLet s find the volume of this cone. Again we can leave our answer in terms of pi or use 3.14 to approximate the answer.
8.5 Volume of Rounded Objects A basic definition of volume is how much space an object takes up. Since this is a threedimensional measurement, the unit is usually cubed. For example, we might talk about
More informationCalculating Perimeter
Calculating Perimeter and Area Formulas are equations used to make specific calculations. Common formulas (equations) include: P = 2l + 2w perimeter of a rectangle A = l + w area of a square or rectangle
More informationCrop Circle Math. (Kagan RallyRobin) TSW find the circumference and area of a real life crop circle.
Course: 7 th Grade Math Student Objective (Obj. 4b) TSW find the circumference and area of circles. DETAIL LESSON PLAN Wednesday, February 8 / Thursday, February 9 Lesson 85 Textbook Pages: 394397 Homework
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 informationEconomics of Painting
Economics of Painting The experienced coating engineer and applicator recognizes that the best way to evaluate cost is on a cost per square foot per year basis. To properly make a cost evaluation, consider
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 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 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 informationMATH 110 Landscape Horticulture Worksheet #4
MATH 110 Landscape Horticulture Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As a Landscape Horticulturist,
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 information2. Complete the table to identify the effect tripling the radius of a cylinder s base has on its volume. Cylinder Height (cm) h
Name: Period: Date: K. Williams ID: A 8th Grade Chapter 14 TEST REVIEW 1. Determine the volume of the cylinder. Use 3.14 for. 2. Complete the table to identify the effect tripling the radius of a cylinder
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 informationThink About This Situation
Think About This Situation A popular game held at fairs or parties is the jelly bean guessing contest. Someone fills a jar or other large transparent container with a known quantity of jelly beans and
More information93. Area of Irregular Figures Going Deeper EXPLORE. Essential question: How do you find the area of composite figures? Area of a Composite Figure
Name Class Date 93 1 Area of Irregular Figures Going Deeper Essential question: How do you find the area of composite figures? CC.7.G.6 EXPLORE Area of a Composite Figure video tutor Aaron was plotting
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 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 informationThe formula for the area of a parallelogram is: A = bh, where b is the length of the base and h is the length of the height.
The formula for the area of a parallelogram is: A = h, where is the length of the ase and h is the length of the height. The formula for the area of a parallelogram is: A = h, where is the length of the
More informationExample 1: If the sum of seven and a number is multiplied by four, the result is 76. Find the number.
EXERCISE SET 2.3 DUE DATE: STUDENT INSTRUCTOR: 2.3 MORE APPLICATIONS OF LINEAR EQUATIONS Here are a couple of reminders you may need for this section: perimeter is the distance around the outside of the
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 informationName: School Team: X = 5 X = 25 X = 40 X = 0.09 X = 15
7th/8th grade Math Meet Name: School Team: Event : Problem Solving (no calculators) Part : Computation ( pts. each) ) / + /x + /0 = X = 5 ) 0% of 5 = x % of X = 5 ) 00  x = ()()(4) + 6 X = 40 4) 0.6 x
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 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 informationFormulas for Area Area of Trapezoid
Area of Triangle Formulas for Area Area of Trapezoid Area of Parallelograms Use the formula sheet and what you know about area to solve the following problems. Find the area. 5 feet 6 feet 4 feet 8.5 feet
More informationGrade 5 Work Sta on Perimeter, Area, Volume
Grade 5 Work Sta on Perimeter, Area, Volume #ThankATeacher #TeacherDay #TeacherApprecia onweek 6. 12. Folder tab label: RC 3 TEKS 5(4)(H) Perimeter, Area, and Volume Cover: Reporting Category 3 Geometry
More informationACTIVITY: Finding a Formula Experimentally. Work with a partner. Use a paper cup that is shaped like a cone.
8. Volumes of Cones How can you find the volume of a cone? You already know how the volume of a pyramid relates to the volume of a prism. In this activity, you will discover how the volume of a cone relates
More informationJunior Math Circles November 18, D Geometry II
1 University of Waterloo Faculty of Mathematics Junior Math Circles November 18, 009 D Geometry II Centre for Education in Mathematics and Computing Twodimensional shapes have a perimeter and an area.
More informationDATE PERIOD. Estimate the product of a decimal and a whole number by rounding the Estimation
A Multiplying Decimals by Whole Numbers (pages 135 138) When you multiply a decimal by a whole number, you can estimate to find where to put the decimal point in the product. You can also place the decimal
More informationThe teacher gives the student a ruler, shows her the shape below and asks the student to calculate the shape s area.
Complex area Georgia is able to calculate the area of a complex shape by mentally separating the shape into familiar shapes. She is able to use her knowledge of the formula for the area of a rectangle
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 informationRight Prisms Let s find the surface area of the right prism given in Figure 44.1. Figure 44.1
44 Surface Area The surface area of a space figure is the total area of all the faces of the figure. In this section, we discuss the surface areas of some of the space figures introduced in Section 41.
More informationInv 1 5. Draw 2 different shapes, each with an area of 15 square units and perimeter of 16 units.
Covering and Surrounding: Homework Examples from ACE Investigation 1: Questions 5, 8, 21 Investigation 2: Questions 6, 7, 11, 27 Investigation 3: Questions 6, 8, 11 Investigation 5: Questions 15, 26 ACE
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 informationCircumference of a Circle
Circumference of a Circle A circle is a shape with all points the same distance from the center. It is named by the center. The circle to the left is called circle A since the center is at point A. If
More informationArea is a measure of how much space is occupied by a figure. 1cm 1cm
Area Area is a measure of how much space is occupied by a figure. Area is measured in square units. For example, one square centimeter (cm ) is 1cm wide and 1cm tall. 1cm 1cm A figure s area is the number
More informationLesson 21. Circles. Objectives
Student Name: Date: Contact Person Name: Phone Number: Lesson 1 Circles Objectives Understand the concepts of radius and diameter Determine the circumference of a circle, given the diameter or radius Determine
More informationDŵr y Felin Comprehensive School. Perimeter, Area and Volume Methodology Booklet
Dŵr y Felin Comprehensive School Perimeter, Area and Volume Methodology Booklet Perimeter, Area & Volume Perimeters, Area & Volume are key concepts within the Shape & Space aspect of Mathematics. Pupils
More informationMAT104: Fundamentals of Mathematics II Summary of Section 145: Volume, Temperature, and Dimensional Analysis with Area & Volume.
MAT104: Fundamentals of Mathematics II Summary of Section 145: Volume, Temperature, and Dimensional Analysis with Area & Volume For prisms, pyramids, cylinders, and cones: Volume is the area of one base
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 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 informationSurface Area of Prisms
Surface Area of Prisms Jen Kershaw Say Thanks to the Authors Click http://www.ck12.org/saythanks (No sign in required) To access a customizable version of this book, as well as other interactive content,
More informationPseudocode, Flowcharts and Python
3 Pseudocode, Flowcharts and Python In Chapter 2, we learned how to store information in the computer and the rules governing the manipulation of numbers and logical values. Now we will look at how to
More informationArea & Volume. 1. Surface Area to Volume Ratio
1 1. Surface Area to Volume Ratio Area & Volume For most cells, passage of all materials gases, food molecules, water, waste products, etc. in and out of the cell must occur through the plasma membrane.
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 informationHeight. Right Prism. Dates, assignments, and quizzes subject to change without advance notice.
Name: Period GL UNIT 11: SOLIDS I can define, identify and illustrate the following terms: Face Isometric View Net Edge Polyhedron Volume Vertex Cylinder Hemisphere Cone Cross section Height Pyramid Prism
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 informationMATH STUDENT BOOK. 6th Grade Unit 8
MATH STUDENT BOOK 6th Grade Unit 8 Unit 8 Geometry and Measurement MATH 608 Geometry and Measurement INTRODUCTION 3 1. PLANE FIGURES 5 PERIMETER 5 AREA OF PARALLELOGRAMS 11 AREA OF TRIANGLES 17 AREA OF
More informationCovering and Surrounding: Homework Examples from ACE
Covering and Surrounding: Homework Examples from ACE Investigation 1: Extending and Building on Area and Perimeter, ACE #4, #6, #17 Investigation 2: Measuring Triangles, ACE #4, #9, #12 Investigation 3:
More informationPlatonic Solids. Some solids have curved surfaces or a mix of curved and flat surfaces (so they aren't polyhedra). Examples:
Solid Geometry Solid Geometry is the geometry of threedimensional space, the kind of space we live in. Three Dimensions It is called threedimensional or 3D because there are three dimensions: width,
More information