# 10-3 Area of Parallelograms

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 0-3 Area of Parallelograms MAIN IDEA Find the areas of parallelograms. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.). 6.G. Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi, and trapezoids) and develop formulas. Also addresses 6.G.3, 6.G., 6.M.7, 6.M.8. New Vocabulary base height NY Math Online glencoe.com Extra Examples Personal Tutor Self-Check Quiz Draw and then cut out a length (l ) rectangle as shown. Cut a triangle from one side of the rectangle and move it to the other side to form a parallelogram. base (b) Repeat Steps and with two other rectangles of different dimensions on grid paper. Copy and complete the table below using the three rectangles and three corresponding parallelograms you created. Rectangle Rectangle Rectangle 3 Length (l) Width (w) Parallelogram Parallelogram Parallelogram 3 Base (b) width (w) Height (h) height (h). How does a parallelogram relate to a rectangle?. What part of the parallelogram corresponds to the length of the rectangle? 3. What part corresponds to the rectangle s width?. MAKE A CONJECTURE What is the formula for the area of a parallelogram? In the Mini Lab, you discovered how the area of a parallelogram is related to the area of a rectangle. The base of a parallelogram can be any one of its sides. height base The height is the distance from the base to the opposite side. 53 Chapter 0 Measurement: Perimeter, Area, and Volume

2 To find the area of a parallelogram, multiply the measures of the base and the height. Area of a Parallelogram Key Concept Words The area A of a parallelogram is the product of any base b and its height h. Model h b Symbols A = bh Find Areas of Parallelograms Find the area of each parallelogram. The base is 6 units, and the height is 8 units. Reading Math Area Measurement An area measurement can be written using abbreviations and an exponent of. For example: square units = units square inches = in square feet = ft square meters = m A = bh Area of parallelogram A = 6 8 Replace b with 6 and h with 8. A = 8 Multiply. The area is 8 square units or 8 units. Estimate A 0 0 or 00 cm cm 3 cm 0 cm A = bh Area of parallelogram A = 0 Replace b with 0 and h with. A = 0 Multiply. The area is 0 square centimeters or 0 cm. Check for Reasonableness Compare 0 with the estimate a. b. 7 m 6 m m Lesson 0-3 Area of Parallelograms 535

3 Height of Parallelograms For the parallelogram formed by the area shaded black in Example 3, its height, inches, is labeled outside the parallelogram. 3 FLAGS Romilla is doing a research project on the nation of Trinidad and Tobago. Part of the project is to paint a replica of the nation s flag. Find the area of the flag that is black. in. 3 6 in. The area of the flag that is black is shaped like a parallelogram, so use the formula A = bh. A = bh Area of parallelogram A = 6 3_ 3_ Replace b with 6 and h with. A = 8 6 3_ = _ 7, or 8 The area of the flag that is black is 8 square inches. c. ART Guadalupe and her dad made parallelogram-shaped picture frames to display some of her artwork. Find the area of the artwork that will be visible in each picture frame..7 cm 8. cm Examples, (p. 535) Find the area of each parallelogram... 0 ft 3. 5 ft 8 m 7 m m Example 3 (p. 536). Find the area of a parallelogram with base 5 yards and height _ 3 yards. 5. TANGRAMS The size of the parallelogram piece in a set of tangrams is shown at the right. Find the area of the piece. 6 cm 5. cm.6 cm 536 Chapter 0 Measurement: Perimeter, Area, and Volume

4 HOMEWORK HELP For Exercises 6 5 HELP See Examples, 3 Find the area of each parallelogram cm 9 cm cm 9. m m in. 5 in. 37 ft ft in.. Find the area of a parallelogram with base feet and height _ feet. 3. Find the area of a parallelogram with base 6.75 meters and height.8 meters.. PARKING Find the area of the parking space below. 5. MAPS What is the area of the region shown on the map? 8.75 mi 8 ft 6.5 mi Livingston Ontario Yates Seneca Steuben 9 ft Find the area of the shaded region in each figure ft 7. ft ft ft 6 cm 8 cm 6 cm 5 cm 8. BUILDINGS The base of a building is shaped like a parallelogram. The first floor has an area of 0,000 square feet. If the base of this parallelogram is 50 feet, can its height be 70 feet? Explain. NYSCC NYSMT Extra Practice, pp. 698, ANALYZE TABLES An architect designed three different parallelogram-shaped brick patios. Find the missing dimensions in the table. Patio Base (ft) Height (ft) Area (ft ) 5 3_ _ 3 0 _ 7 0 5_ 8 3_ 5 6 Lesson 0-3 Area of Parallelograms 537

5 H.O.T. Problems 0. REASONING Refer to parallelogram KLMN at the right. If the area of parallelogram KLMN is 35 square inches, what is the area of triangle KLN?. OPEN ENDED On grid paper, draw three different parallelograms that each have an area of units and a height of units. Compare and contrast the parallelograms.. CHALLENGE If x = 5 and y < x, which figure has the greater area? Explain your reasoning. WRITING IN 3. MATH Explain how the formula for the area of a parallelogram is related to the formula for the area of a rectangle. x y x y NYSMT PRACTICE 6.A.6, 6.G.. Robert used a piece of poster board shaped like a parallelogram to make a sign for his campaign as class president. The base of the poster board is 5 inches, and the area is,87 square inches. Find the height of the poster board. A 88 in. B 76 in. C in. D 36 in. 5. A family has a flower garden in the shape of a parallelogram in their backyard. They planted grass in the rest of the yard. What is the area of the backyard that is planted with grass? 75 ft ft Backyard 5 ft 0 ft F 390 sq ft G 8,90 sq ft H 9,060 sq ft J 9, sq ft Estimate the circumference of each circle. (Lesson 0-) 6. d = 5 in. 7. r = 9 m 8. d = 6 ft 9. MONUMENTS The Lincoln Memorial is a rectangular structure whose base is 88 feet by 8 feet. What is the perimeter of the base of the Lincoln Memorial? (Lesson 0-) PREREQUISITE SKILL Find the value of each expression. (Lesson -) 30. _ _ 5 3. _ _ 538 Chapter 0 Measurement: Perimeter, Area, and Volume

6 0- Area of Triangles MAIN IDEA Find the areas of triangles. NYS Core Curriculum 6.A.6 Evaluate formulas for given input values (circumference, area, volume, distance, temperature, interest, etc.). 6.G. Determine the area of triangles and quadrilaterals (squares, rectangles, rhombi, and trapezoids) and develop formulas. Also addresses 6.G.3, 6.G., 6.M.7, 6.M.8. NY Math Online glencoe.com Concepts in Motion Extra Examples Personal Tutor Self-Check Quiz BIOSPHERE The structure of the different sections in the Biosphere complex in Tucson, Arizona, are made of interlocking triangles that are all the same size.. Compare the two outlined triangles.. What figure is formed by the two triangles? 3. MAKE A CONJECTURE Describe the relationship that exists between the area of one triangle and the area of the parallelogram. A parallelogram can be formed by two congruent triangles. Since congruent triangles have the same area, the area of a triangle is one half the area of the parallelogram. The base of a triangle can be any one of its sides. The height is the shortest distance from a base to the opposite vertex. height (h) base (b) Area of a Triangle Key Concept Words The area A of a triangle is one half the product of the base b and its height h. Symbols A = _ bh or A = _ bh Model h b Find the Area of a Triangle Find the area of each triangle. height base By counting, you find that the measure of the base is 6 units and the height is units. 50 Chapter 0 Measurement: Perimeter, Area, and Volume

7 Mental Math You can use mental math to multiply _ (6)(). Think: Half of 6 is 3, and 3 is. A = _ bh Area of a triangle A = _ (6)() Replace b with 6 and h with. A = _ () Multiply. A = Multiply. The area of the triangle is square units.. m 6. m Check for Reasonableness To estimate the area of the triangle in Example, round the base to meters and the height to 6 meters. The area is then _ 6 or 36 square meters. Since 38.7 is close to 36, the answer is reasonable. A = _ bh Area of a triangle A = _ (.)(6.) Replace b with 7 and h with 9. A = _ (77.) Multiply. A = 38.7 Divide. _ (77.) = 77., or 38.7 The area of the triangle is 38.7 square meters. a. b. 9 ft 7 ft 3 TENTS The front of a two-person camping tent has the dimensions shown. How much material was used to make the front of the tent? A = _ bh Area of a triangle A = _ (5)(3) Replace b with 5 and h with 3. A = _ (5) or 7.5 Multiply. The front of the tent has an area of 7.5 square feet. 5 ft 3 ft c. SNACKS A triangular cracker has a height of centimeters and a base of 5 centimeters. Find the area of the cracker. Lesson 0- Area of Triangles 5

8 Examples, (pp. 50 5) Find the area of each triangle... 8 ft 3..5 m ft 5.6 m Example 3 (p. 5). CRAFTS Consuela made a triangular paper box as shown. What is the area of the top of the box? 9 cm 0 cm For Exercises 5, 6 7 3, HELP HOMEWORK HELP See Examples 3 Find the area of each triangle in. 9 in cm.8 cm 9. 5 m 7 m ft ft. height: in., base: 35 in.. height: 7 cm, base: 9 cm 3. ROOFING Ansley is going to help his father shingle the roof of their house. What is the area of the triangular portion of one end of the roof to be shingled? yd 7 yd. ARCHITECTURE An architect plans on designing a building on a triangular plot of land. If the base of the triangle is 00.8 feet and the height is 96.3 feet, find the available floor area the architect has to design the building. 5. FLOWER BEDS A flower bed in a parking lot is shaped like a triangle as shown. Find the area of the flower bed in square feet. If one bag of topsoil covers 0 square feet, how many bags are needed to cover this flower bed? 3 yd yd 5 Chapter 0 Measurement: Perimeter, Area, and Volume

9 6. ALGEBRA The table at the right shows the areas of a triangle where the base of the triangle stays the same but the height changes. Write an algebraic expression that can be used to find the area of a triangle that has a base of 5 units and a height of n units. 7. REASONING Which is smaller, a triangle with an area of square foot or a triangle with an area of 6 square inches? 8. FLAGS What is the area of the triangle on the flag of the Philippines at the right? 30 in. Base (units) Area of Triangles Height (units) Area (units ) n 3 ft COMPOSITE FIGURES Find the perimeter and area of each figure. 9. in mm 9 mm 5 ft 6 mm NYSCC NYSMT Extra Practice, pp. 699, 75 in. 5 in. 5 in. 8 mm 0 mm 8 mm 0 mm 9 mm H.O.T. Problems. FIND THE ERROR Dolores and Demetrius are finding the base of the triangle shown. Its area is 8.5 square meters. Who is correct? Explain. 00 = _ (b)(0) 00 = 0b 0 = b 00 = (b)0 00 = 0b 5 = b b m 0 m Dolores CHALLENGE For Exercises 5, use the information below. All the triangles and squares in the quilt pattern shown are congruent.. Find the measure of the base and height of one of the triangles. 3. Calculate the area of one triangle and then find the area of all the triangles.. Calculate the area of one of the smaller squares and then find the area of all of the smaller squares. Demetrius in. 5. What is the total area of the figure? Is your answer reasonable? in. Lesson 0- Area of Triangles 53

10 6. REASONING If two triangles have an area of square feet, do they always have the same base and height? Use a model to explain your answer. WRITING IN 7. MATH Draw a triangle and label its base and height. Draw another triangle that has the same base, but a height twice that of the first triangle. Find the area of each triangle. Then write a ratio that expresses the area of the first triangle to the area of the second triangle. NYSMT PRACTICE 6.A.6, 6.G. 8. The table below shows the areas of a triangle where the height of the triangle stays the same but the base changes. Height (units) Areas of Triangles Base (units) Area (square units) _ _ 7 x? Which expression can be used to find the area of a triangle that has a height of 7 units and a base of x units? A 7x B 7x_ C 7 _ D x _ 9. Norma cut a triangle out of construction paper for an art project. h cm 3 cm The area of the triangle is 8.5 square centimeters. What is the height of the triangle? F 6.5 cm G 3 cm H 6 cm J 69 cm 30. Find the area of a parallelogram with base 5 inches and height 0 inches. (Lesson 0-3) 3. Find the circumference of a circle with a radius of 5 meters. Round to the nearest tenth. (Lesson 0-) 3. IDENTIFICATION Measure the length and width of a student ID card or library card to the nearest eighth inch. Then find the perimeter of the card. (Lessons -9 and 0-) 33. PREREQUISITE SKILL A bookstore arranges its best-seller books in the front window. In how many ways can four best-seller books be arranged in a row? Use the act it out strategy. (Lesson 5-3) 5 Chapter 0 Measurement: Perimeter, Area, and Volume

### MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 18 units.

1-9 Algebra: Area Formulas MAIN IDEA The rectangle at the right has an area of 20 square units. The distance around the rectangle is 5 + 4 + 5 + 4, or 1. Find the areas of rectangles and squares. New Vocabulary

### Perimeter, Area, and Volume

CHAPTER 9 connected.mcgraw-hill.com Investigate Animations Vocabulary Multilingual eglossary Perimeter, Area, and Volume The BIG Idea What is the relationship between the circumference and diameter of

### Area Long-Term 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

### Characteristics 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.

### Perimeter, 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

### Area 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

### 11-1 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

### Perimeter 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

### Area 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

### Tallahassee 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

### Each 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

### Signs, 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,

### Circumference and Area of Circles

ircumference and Area of ircles 7- MAIN IDEA Measure and record the distance d across the circular part of an object, such as a battery or a can, through its center. Find the circumference and area of

### Area and Circumference

4.4 Area and Circumference 4.4 OBJECTIVES 1. Use p to find the circumference of a circle 2. Use p to find the area of a circle 3. Find the area of a parallelogram 4. Find the area of a triangle 5. Convert

### Show 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

### Calculating 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

### Model area formulas for parallelograms, trapezoids, and triangles.

Answers Teacher Copy Lesson 23-3 Area of Triangles, Trapezoids, and Polygons Learning Targets p. 297 Model area formulas for parallelograms, trapezoids, and triangles. Write equations that represent problems

### Math Tech 1 Unit 11. Perimeter, Circumference and Area. Name Pd

Math Tech 1 Unit 11 Perimeter, Circumference and Area Name Pd 11-1 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

### 11-6 Area: Parallelograms, Triangles, and Trapezoids

1. 6. LACROSSE A lacrosse goal with net is shown. The goal is 6 feet wide, 6 feet high, and 7 feet deep. What is the area of the triangular region of the ground inside the net? 30.5 ft 2 2. 21 ft 2 14.08

### 11-2 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 4-H Club. Her first project is to make a simple A-line

### How 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 pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

### Hands-On Mini Lab. Step 2 Pick one vertex and draw a segment to the opposite vertex. The angles of a quadrilateral have a special relationship.

10-7 Quadrilaterals MAIN IDEA I will classify quadrilaterals and find missing angle measures in quadrilaterals. New Vocabulary quadrilateral rectangle square ogram trapezoid Hands-On Mini Lab The figure

### 12-4 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

### Teacher Page Key. Geometry / Day # 13 Composite Figures 45 Min.

Teacher Page Key Geometry / Day # 13 Composite Figures 45 Min. 9-1.G.1. Find the area and perimeter of a geometric figure composed of a combination of two or more rectangles, triangles, and/or semicircles

### 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

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

### Perimeter, 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

### Geometry 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

### Volume of Spheres. A geometric plane passing through the center of a sphere divides it into. into the Northern Hemisphere and the Southern Hemisphere.

Page 1 of 7 9.6 Surface Area and Volume of Spheres Goal Find surface areas and volumes of spheres. Key Words sphere hemisphere A globe is an example of a sphere. A sphere is the set of all points in space

### 9-3. 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 9-3 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

### MATH 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

### VOLUME 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:

### LESSON 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 one-dimension and two-dimensions. In the next lesson,

### WHAT IS AREA? CFE 3319V

WHAT IS AREA? CFE 3319V OPEN CAPTIONED ALLIED VIDEO CORPORATION 1992 Grade Levels: 5-9 17 minutes DESCRIPTION What is area? Lesson One defines and clarifies what area means and also teaches the concept

### YOU 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

### Rectangle Square Triangle

HFCC Math Lab Beginning Algebra - 15 PERIMETER WORD PROBLEMS The perimeter of a plane geometric figure is the sum of the lengths of its sides. In this handout, we will deal with perimeter problems involving

### Name: Date: Geometry Honors Solid Geometry. Name: Teacher: Pd:

Name: Date: Geometry Honors 2013-2014 Solid Geometry Name: Teacher: Pd: Table of Contents DAY 1: SWBAT: Calculate the Volume of Prisms and Cylinders Pgs: 1-6 HW: Pgs: 7-10 DAY 2: SWBAT: Calculate the Volume

### 12-2 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

### Geometry 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 LT9-1: Solve problems involving the perimeter and area of

### POOLS The diagram of the pool from the beginning of the lesson is shown below. Find the area of the pool s floor. 28 ft. 6 ft. 4 ft.

Multi-Part Lesson 9-3 PART Main Idea Find areas of composite figures. glencoe.com Composite Figures A C B D Area of Composite Figures 8 ft POOLS The dimensions of a pool at recreation center are shown..

### Perimeter 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,

### Similar Polygons. Copy both triangles onto tracing paper. Measure and record the sides of each triangle. Cut out both triangles.

-7 Similar Polygons MAIN IDEA Identify similar polygons and find missing measures of similar polygons. New Vocabulary polygon similar corresponding parts congruent scale factor Math Online glencoe.com

### Geometry 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

### Perimeter, Circumference, Area and Ratio Long-Term 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

### 17.2 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

### Lesson 12.1 Skills Practice

Lesson 12.1 Skills Practice Name Date Introduction to Circles Circle, Radius, and Diameter Vocabulary Define each term in your own words. 1. circle A circle is a collection of points on the same plane

### Calculating 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

### 12.3. Model Perimeter Formulas. Unlock the Problem. Essential Question. Name

? Name 12.3 Essential Question Model Perimeter Formulas How can you use a formula to find the perimeter of a rectangle? lgebraic Reasoning 4.5., 4.5. MTHEMTIL PROESSES 4.1., 4.1.F Unlock the Problem Julio

### Perimeter 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

### Geometry 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 (LT-1) Solve problems involving the perimeter and area of triangles

### Integrated 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

### Section 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

### Perimeter. 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

### Student Outcomes. Lesson Notes. Classwork. Exercises 1 3 (4 minutes)

Student Outcomes Students give an informal derivation of the relationship between the circumference and area of a circle. Students know the formula for the area of a circle and use it to solve problems.

### Perimeter, Circumference, and Area KEY

Notes The perimeter of a polygon is the total distance around a polygon. Although there are formulas for finding the perimeter of a rectangle (2l + 2w) and for the square (4s), perimeter for any polygon

### 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

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:

### Number Models for Area

Number Models for Area Objectives To guide children as they develop the concept of area by measuring with identical squares; and to demonstrate how to calculate the area of rectangles using number models.

### Study 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

### Functional Skills Mathematics

Functional Skills Mathematics Level Learning Resource Perimeter and Area MSS1/L.7 Contents Perimeter and Circumference MSS1/L.7 Pages 3-6 Finding the Area of Regular Shapes MSS1/L.7 Page 7-10 Finding the

### 11-4 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:,

### Circumference 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

### 28. [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

### PERIMETER AND AREA. In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures.

PERIMETER AND AREA In this unit, we will develop and apply the formulas for the perimeter and area of various two-dimensional figures. Perimeter Perimeter The perimeter of a polygon, denoted by P, is the

### 12-1 Representations of Three-Dimensional Figures

Connect the dots on the isometric dot paper to represent the edges of the solid. Shade the tops of 12-1 Representations of Three-Dimensional Figures Use isometric dot paper to sketch each prism. 1. triangular

### 43 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

### Geometry: Chapter Questions. 1. How is the formula for area of a parallelogram related to area of a rectangle?

Geometry: Chapter Questions. How is the formula for area of a parallelogram related to area of a rectangle?. How is the formula for area of a triangle related to area of a rectangle?. How do you find the

### TEKS TAKS 2010 STAAR RELEASED ITEM STAAR MODIFIED RELEASED ITEM

7 th Grade Math TAKS-STAAR-STAAR-M Comparison Spacing has been deleted and graphics minimized to fit table. (1) Number, operation, and quantitative reasoning. The student represents and uses numbers in

### Lesson 13.1. Perimeter Essential Question How can you use a formula to find the perimeter of a rectangle? Unlock the Problem. Math Talk.

Name Perimeter Essential Question How can you use a formula to find the perimeter of a rectangle? Lesson 13.1 Measurement and Data 4.MD.A.3 MATHEMATICAL PRACTICES MP1, MP7, MP8 Unlock the Problem Julio

### Basic Math for the Small Public Water Systems Operator

Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the

### 3. 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

### Chapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green Worked-Out Solutions. Try It Yourself (p. 353) Number of cubes: 7

Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.

### Geometry 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

### 6.3. Surface Area of Solids The Gift Box. My Notes ACTIVITY

Surface Area of Solids SUGGESTED LEARNING STRATEGIES: Activating Prior Knowledge J.T. is the creative director for a paper products company. The company is introducing a new line of gift boxes, called

### Area and Perimeter. Practice: Find the perimeter of each. Square with side length of 6 cm. Rectangle with side lengths of 4 cm and 7 cm

Area and Perimeter Perimeter: add up all the sides (the outside of the polygon) Practice: Find the perimeter of each Square with side length of 6 cm Rectangle with side lengths of 4 cm and 7 cm Parallelogram

### Geometry. 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

### Formulas 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

### Area and Perimeter. Name: Class: Date: Short Answer

Name: Class: Date: ID: A Area and Perimeter Short Answer 1. The squares on this grid are 1 centimeter long and 1 centimeter wide. Outline two different figures with an area of 12 square centimeters and

### How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures

.6 Perimeters and Areas of Similar Figures How do changes in dimensions of similar geometric figures affect the perimeters and the areas of the figures? ACTIVITY: Creating Similar Figures Work with a partner.

### Assessment Management

Areas of Rectangles Objective To reinforce students understanding of area concepts and units of area. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts Workshop Game Family

### G6-9 Area of Composite Shapes

G6-9 Area of Composite Shapes 1. a) Calculate the area of each figure. b) Draw a line to show how Shape C can be divided into rectangles A and. i) ii) A C A C Area of A = Area of A = Area of = Area of

### Family Letters. Assessment Management. Playing Fraction Of

Formula for the Area of a Parallelogram Objectives To review the properties of parallelograms; and to guide the development and use of a formula for the area of a parallelogram. www.everydaymathonline.com

### Chapter 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

### Sect 9.5 - Perimeters and Areas of Polygons

Sect 9.5 - Perimeters and Areas of Polygons Ojective a: Understanding Perimeters of Polygons. The Perimeter is the length around the outside of a closed two - dimensional figure. For a polygon, the perimeter

### Grade 3 Math Expressions Vocabulary Words

Grade 3 Math Expressions Vocabulary Words Unit 1, Book 1 Place Value and Multi-Digit Addition and Subtraction OSPI words not used in this unit: add, addition, number, more than, subtract, subtraction,

### CIRCUMFERENCE AND AREA OF CIRCLES

CIRCUMFERENCE AND AREA F CIRCLES 8..1 8.. Students have found the area and perimeter of several polygons. Next they consider what happens to the area as more and more sides are added to a polygon. By exploring

### Area 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

### Area and Volume Equations

Area and Volume Equations MODULE 16? ESSENTIAL QUESTION How can you use area and volume equations to solve real-world problems? LESSON 16.1 Area of Quadrilaterals 6.8.B, 6.8.D LESSON 16. Area of Triangles

### Perimeter and Area. Chapter 11 11.1 INTRODUCTION 11.2 SQUARES AND RECTANGLES TRY THESE

PERIMETER AND AREA 205 Perimeter and Area Chapter 11 11.1 INTRODUCTION In Class VI, you have already learnt perimeters of plane figures and areas of squares and rectangles. Perimeter is the distance around

### Perimeter, Circumference, and Area

-9 Perimeter, Circumference, and Area -9. Plan What You ll Learn To find perimeters of rectangles and squares, and circumferences of circles To find areas of rectangles, squares, and circles... And Why

### 2006 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

Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. 1. 5. KALEIDOSCOPE The kaleidoscope image shown is a regular polygon with 14 sides. What

### SA 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.

### Perimeter and Area. Rectangle rectángulo a quadrilateral with four right. angles; opposite sides are equal and parallel.

CHAPTER 11 Perimeter and Area connected.mcgraw-hill.com Investigate Animations Vocabulary Math Songs The BIG Idea How do I find the perimeter of polygons? How can I use the area formula for a rectangle

Section 7.2 Quadratic Applications Now that you are familiar with solving quadratic equations it is time to learn how to apply them to certain situations. That s right, it s time for word problems. The

### Algebra 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:

### Geometry: Measuring Area and Volume

C H A P T E R Geometry: Measuring Area and Volume 3 33 Aaron Haupt How is math used in packaging candy? When marketing a product such as candy, how the product is packaged can be as important as how it

### Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms.

Volume of Rectangular Prisms Objective To provide experiences with using a formula for the volume of rectangular prisms. www.everydaymathonline.com epresentations etoolkit Algorithms Practice EM Facts

### Postulate 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) 11-1: 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

### Grade 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