All the solutions provided inMcGraw Hill My Math Grade 3 Answer Key PDF Chapter 13 Lesson 8 Area of Composite Figures will give you a clear idea of the concepts.
McGraw-Hill My Math Grade 3 Answer Key Chapter 13 Lesson 8 Area of Composite Figures
A composite figure is made up of two or more figures. To find the area of a composite figure, decompose the figure into smaller parts.
Math in My World
Example 1
Shrubs, trees, flowers, and plants can be bought at Mr. Corley’s Nursery. What is the area of the nursery’s garden at the right?
1. Break the composite figure into smaller parts. Look for rectangles.
2. Find the area of each part.
Rectangle 1
A = l × w
= 10 × 8
= ______________
Answer:
A = l × w
= 10 × 8
= 80
Rectangle 2
A = l × w
= 12 × 8
= (10 × 8) + (2 × 8) Decompose 12 as 10 + 2.
= _________ + ____________
= ___________
The area of Rectangle 1 is ______________ square yards. The area of Rectangle 2 is ______________ square yards.
Answer:
A = l × w
= 12 × 8
= (10 × 8) + (2 × 8) Decompose 12 as 10 + 2.
= 80 + 16
= 96
The area of Rectangle 1 is 96 square yards. The area of Rectangle 2 is 96 square yards.
3. Add the areas.
80 + 96 = _______________
The area of the composite figure is _______________ square yards.
Answer:
80 + 96 = 176
The area of the composite figure is 176 square yards.
Example 2
Find the area of the composite figure.
1. Break the composite figure into smaller parts. Look for rectangles.
This composite figure can be broken into _____________ rectangles.
2. Find the area of each part. Rectangles 2 and 3 are the same size.
Rectangle 1
A = l × w
= 12 × 2
= (10 × 2) + (2 × 2) Decompose 12
= _________ + ____________
= ___________ square meters
Rectangles 2 and 3
A = l × w
= 8 × 3
= ______________ square meters
3. Add the areas. 24 + 24 + 24 = ___________
The area of the composite figure is _____________ square meters.
Answer:
A = l × w
= 12 × 2
= (10 × 2) + (2 × 2) Decompose 12
= 20 + 4
= 24 square meters
A = l × w
= 8 × 3
= 24 square meters
Add the areas. 24 + 24 + 24 = 72
The area of the composite figure is 72 square meters.
Talk Math
Refer to Example 1. Find another way to decompose the composite figure.
Answer:
Decompose the figure into two rectangles, find their sum, and then subtract the area of the removed corner. A composite figure has three congruent triangles removed from it.
Guided Practice
Question 1.
Find the area of the composite figure. Show your work.
The area is _____________ square centimeters.
Answer:
Rectangle 1:
A = l × w
7 × 3 = 21 sq. cm
A = l × w
4 × 2 = 8 sq. cm
A = 21 + 8 = 29 sq. cm
The area is 29 square centimeters.
Independent Practice
Find the area of each composite figure. Show your work.
Question 2.
The area is _____________ square feet.
Answer:
A = l × w
A = 4 × 10 = 40 sq. ft
A = l × w
A = 9 × 8 = 72 sq. ft
A = 40 + 72 = 112
The area is 112 square feet.
Question 3.
The area is _____________ square meters.
Answer:
A = l × w
A = 10 × 2 = 20 sq. m
A = 5 × 3 = 15 sq. m
A = 20 + 15 = 35 sq. m
The area is 35 square meters.
Question 4.
The area is _______________.
Answer:
A = l × w
A = 3 × 6 = 18
A = 1 × 3 = 3
A = 18 + 3 = 21 sq. ft
The area is 21 sq. ft.
Question 5.
The area is _______________.
Answer:
A = l × w
A = 2 × 11 = 22
A = 4 × 9 = 36
A = 22 + 36 = 58
The area is 58 sq. yd.
Question 6.
Decompose the composite figure in Exercise 4 a different way. Show the steps you used.
Answer:
6 × 2 = 12
9 × 1 = 9
Total area = 12 + 9 = 21
Problem Solving
Question 7.
What is the area of the top of the desk?
Answer:
Rectangle 1
2 × 3 = 6
Rectangle 2
2 × 3 = 6
Rectangle 3
2 × 1 = 2
6 + 6 + 2 = 14 sq. ft
Question 8.
Mathematical PRACTICE Make a Plan Courtney is playing miniature golf. What is the area of the composite figure?
Answer:
Rectangle 1:
4 × 2 = 8
Rectangle 2:
4 × 3 = 12
Rectangle 3:
2 × 1 = 2
Total area = 8 + 12 + 2 = 22 sq. ft
HOT Problems
Question 9.
Mathematical PRACTICE Model Math Draw and label two composite figures that have the same area but have different perimeters.
Answer:
3 × 1 = 3
2 × 2 = 4
A = 3 + 4 = 7
P = 11
4 × 1 = 4
3 × 1 = 3
A = 4 + 3 = 7
P = 18
Question 10.
Building on the Essential Question How is the operation of addition related to finding the area of a composite figure?
Answer:
First you find area of the rectangle. Then you find the second area and add both rectangles together.
McGraw Hill My Math Grade 3 Chapter 13 Lesson 8 My Homework Answer Key
Practice
Find the area of each composite figure. Show your work.
Question 1.
The area is _______________ square centimeters.
Answer:
Rectangle 1:
A = l × w
12 × 3 = 36
Rectangle 2:
A = l × w
A = 4 × 3 = 12
Total area = 36 + 12 = 48
The area is 48 square centimeters.
Question 2.
The area is _______________ square meters.
Answer:
Rectangle 1:
A = l × w
A = 9 × 4 = 36
Rectangle 2:
A = l × w
A = 9 × 9
A = 81
A = 36 + 81 = 117
The area is 117 square meters.
Vocabulary Check
Question 3.
Draw an example of a composite figure.
Answer:
Problem Solving
The composite figure shows the floor plan of a bathroom.
Question 4.
What is the area of the bathroom floor?
Answer:
Rectangle 1:
A = l × w
7 × 8 = 56
Rectangle 2:
A = l × w
11 × 4 = 44
56 + 44 = 100 sq. ft
Question 5.
Mathematical PRACTICE Plan Your Solution The floor will be covered in square tiles. If one square tile covers one square foot. how many tiles are needed?
Answer: 100 tiles are needed
Test Practice
Question 6.
What is the area of the composite figure shown?
(A) 8 square units
(B) 12 square units
(C) 16 square units
(D) 20 square units
Answer: (C) 16 square units
Explanation:
A1 = 2 × 3 = 6
A2 = 3 × 2 = 6
A3 = 2 × 2 = 4
A = 6 + 6 + 4 = 16 sq. units
Option C is the correct answer.
