We included **HMH Into Math Grade 7 Answer Key PDF** **Module 10 Lesson 4 Areas of Composite Figures **to make students experts in learning maths.

## HMH Into Math Grade 7 Module 10 Lesson 4 Answer Key Areas of Composite Figures

I Can break a composite figure into simple shapes and use area formulas to find its area.

**Step It Out**

Question 1.

Rahim drew an outline of the front of a house on grid paper. He wants to find the area of his model.

A. Separate the composite figure into simple geometric figures. What simple geometric figures are used to form the outline?

Answer:

Explanation:

Simple geometric figures rectangle and triangle are used to form the outline of composite figure.

B. Determine the dimensions and then find the area of each of the simple geometric figures.

Answer:

Area of rectangle = 15sq units

Area of triangle = 7 sq units

Explanation:

Area of a rectangle 5 x 3 units

A = length x width

A = 5 x 3 = 15 sq units

Area of a triangle

A = 1/2 base x height

A = 0.5 x 7 x 2

A = 7 sq units

C. Find the area of the composite figure.

Answer:

Area of composite figure = 22 sq units

Explanation:

First find the area of simple figures,

Area of a rectangle 5×3 units

A = length x width

A = 5 x 3 = 15 sq units units

Area of a triangle

A = 1/2 base x height

A = 0.5 x 7 x 2

A = 7 sq units

Area of composite figure = Rectangle are + Triangle area

Total area of the figure = 15 + 7 = 22 sq units

**Turn and Talk** Can you separate the composite figure into different simple geometric figures? Explain.

Answer:

Step 1: Divide the compound shape into known basic shapes.

Step 2: Find the area of each basic shape separately.

Step 3: Add all the areas of basic shapes together.

Step 4: Now, write the answer in square units of the given composite figure.

Question 2.

A section of a basketball court is shown.

A. Determine the simple geometric figures that are used in the composite figure.

Answer:

Rectangle and semicircle.

Explanation:

Rectangle has 2 sides parallel to each other.

Half of the circle is known as circle.

B. Find the dimensions of the simple geometric figures.

Answer:

Explanation:

Given length of the rectangle is 12ft, width of the rectangle is 19ft.

Diameter of circle is 12 ft, radius of circle is d/2 = 12/2 = 6ft.

C. How is the area of a semicircle related to the area of a circle with the same radius?

Answer:

Area = 36π sq ft

Explanation:

diameter = 12 ft

radius = d/2

r = 12/2

r = 6 ft

Area of a semicircle related to the area of a circle with the same radius

A = π x 6 x 6

A = 36π sq ft

D. Find the area of the simple geometric figures to the nearest square foot. Use 3.14 for π.

Answer:

Area = 113.04 sq ft

Explanation:

A = 3.14 x 6 x 6

A = 113.04 sq ft

E. Find the area of the composite figure.

Answer:

Area = 341.04 sq ft

Explanation:

Rectangle area A = length x width

A = 19 x 12

A = 228 sq ft

Area of the composite figure = Rectangle area + Semi circle area

A = 228 + 113.04

A = 341.04 sq ft

**Turn and Talk** What method do you use to determine the simple geometric figures of a composite figure?

Answer:

By splitting the simple geometric figures and then add the areas together.

Explanation:

The method to determine the simple geometric figures of a composite figure

A composite figure is made up of simple geometric shapes.

To find the area of a composite figure or other irregular-shaped figure, divide it into simple, nonoverlapping figures.

Find the area of each simpler figure, and then add the areas together to find the total area of the composite figure.

Question 3.

The manager of a hotel wants to put new carpet in the lobby. The dimensions of the lobby are shown. There is a statue with a circular base in the lobby that does not need to have carpet under it.

A. Determine the simple geometric figures that are in the composite figure. Find the dimensions of the simple geometric figures.

Answer:

Explanation:

Given, diameter of circle is 4ft

Dimensions of rectangular length is 9ft and width is 30ft

Dimensions of triangular length is 6ft and base is 3ft.

B. Find the areas of the simple geometric figures. Use 3.14 for π.

Answer:

Area of circle = 12.56 sq ft

Area of triangle = 9 sq ft

Area of rectangle = 30 x 9 = 270 sq ft

Explanation:

circle area

A = 3.14 x 2 x 2

Area of circle = 12.56 sq ft

Area of triangle

Area of triangle = (1/2) base x height

Area of triangle = 0.5 x 3 x 6

Area of triangle = 9 sq ft

Area of rectangle A(Rectangle) = Length x Width

A(rectangle) = 30 x 9 = 270 sq ft

C. Find the area of the lobby that needs carpet. Explain how you found the area.

Answer:

Area = 275.44 sq ft

Explanation:

The area of the lobby that needs carpet

A = A(rectangle) – A(circle) + 2 A(triangle)

A = 270 – 12.56 + 2 x 9

A = 275.44 sq ft

**Check Understanding**

Question 1.

Find the area of the composite figure.

Answer:

Area = 11 sq units

Explanation:

Area of composite figure

Area of fig A = length x width = 2 x 3 = 6 sq units

Area of fig B = (1/2) base x height = 0.5 x 2 x 1 = 1 sq unit

Area of fig C = (1/2) base x height = 0.5 x 2 x 1 = 1 sq unit

Area of fig D = (1/2) base x height = 0.5 x 2 x 3 = 3 sq unit

Area of composite figure = Area of (A+B+C+D+

A = 6 + 1 + 1 + 3 = 11 sq units

Question 2.

Farrah has a piece of paper that is 11 inches song and 8 inches wide. She cuts a semicircle with a radius of 4 inches out of the piece of paper. What is the area of the piece of paper she has left after the cut to the nearest hundredth? Use 314 for π.

Answer:

Area = 62.88 sq ft

Explanation:

r = 4 in

A = 3.14 x 4 x 4

A = 50.24 sq ft

semi circle = 50.24/2 = 25.12 sq ft

Rectangle area A = length x width

A = 11 x 8

A = 88 sq ft

The area of the piece of paper she has left after the cut to the nearest hundredth

A = 88 – 25.12 sq ft

A = 62.88 sq ft

**On Your Own**

Question 3.

Greg designed a trophy using grid paper. What is the area of the drawing of the trophy shown?

Answer:

Area = 12 sq units

Explanation:

Area of figure A = l x w = 2 x 4 = 8 sq units

Area of figure B =(1/2) x 1 x 3 = 1.5 sq units

Area of figure C = (1/2) x 1 x 3 = 1.5 sq units

Area of figure D = [(1/2) x 1 x 1] 2 = 1 sq units

the drawing of the trophy shown = 8 + 1.5 + 1.5 + 1 = 12 sq units

Question 4.

**Attend to Precision** Clara is making a pennant. She attaches a rectangle that is 1 inch wide and 6 inches long to a triangle that has a base of 6 inches and a height of 28 inches. What is the area of the pennant?

Answer:

Area of the pennant = 6 + 84 = 90 sq in

Explanation:

A rectangle is 1 inch wide and 6 inches long

Area = length x width

A = 6 x 1 = 6 sq in

to a triangle that has a base of 6 inches and a height of 28 inches

A =(1/2) x base x height

A = 0.5 x 6 x 28

A = 84 sq in

the area of the pennant = 6 + 84 = 90 sq in

Question 5.

Financial Literacy Mary is installing carpet in a closet for a customer. A floor plan of the closet is shown, Mary charges $5.60 per square foot of carpet, plus a $150 installation fee.

How much should Mary charge the customer to the nearest cent? Use 3.14 for π.

Answer:

$486

Explanation:

A floor carpet area of the closet is A

A = area of figure A + area of figure B( semi )

Area of figure A

A = (1/2) base x height

A = 0.5 x 7 x 6

A = 21 sq ft

Area of figure B

d = 7 ft

r = d/2 = 7/2 = 3.5 ft

A = 3.14 x 3.5 x 3.5

A = 38.465 sq ft

A = area of figure A + area of figure B

A = 21 + 38.465

A = 59.465 sq ft

A = 60sq ft

Mary charges $5.60 per square foot of carpet, plus a $150 installation fee.

Total cost = 60 x 5.60 + 150

Total cost = 336 + 150 = $486

**For Problems 6-9, find the area of the composite figure shown to the nearest half unit. Use 3.14 for π.**

Question 6.

Answer:

13 sq units

Explanation:

Area of the composite figure is shown above

A = there are 11 complete squares = 11 sq ft

semi parts are 1.5 + 0.5 = 2sq units

Totals area of a given figure is

A = 11 + 2 = 13 sq units

Question 7.

Answer:

8 sq units

Explanation:

Area A = 6 + 2 = 8 sq units

Question 8.

Answer:

23.4675 sq cm

Explanation:

Area of a rectangle = l x w

A = 9 x 3 = 27 sq cm

Area of a semi circle = 1/2 (3.14 x 1.5 x 1.5)

Area of semi circle = 3.5325 sq cm

Area of a given figure is = 27 – 3.5325 sq cm

A = 23.4675 sq cm

Question 9.

Answer:

22 sq in

Explanation:

Area of square = Side x Side

A1 = 4 x 4 = 16 sq in

Area of triangle = 1/2 x base x height

A2 = 0.5 x 1 x 4 = 2 sq in

A3 = 0.5 x 2 x 4 = 4 sq in

A = A1 + A2 + A3

A = 16 + 2 + 4

A = 22 sq in

**Lesson 10.4 More Practice/Homework**

Question 1.

A driveway consists of two rectangles. One rectangle is 80 feet long and 15 feet wide. The other is 30 feet long and 30 feet wide. What is the area of the driveway?

Answer:

2100 sq ft

Explanation:

A rectangle is 15 ft wide and 80 inches long

Area = length x width

A1 = 80 x 15 = 1200 sq ft

A rectangle is 30 ft wide and 30 inches long

Area = length x width

A2 = 30 x 30 = 900 sq ft

the area of the driveway

A = A1 + A2

A = 1200 + 900

A = 2100 sq ft

Question 2.

**Use Tools** A patio is made of two sections. One is shaped like a trapezoid, and the other like a semicircle. The bases of the trapezoid are 12 feet and 8 feet. The height of the trapezoid is 4 feet. The diameter of the semicircle is the same as the trapezoid’s shorter base. Use geometry software or another tool to draw a model of the patio. Find the patio’s area. Use 3.14 for π.

Answer:

72.56 sq ft

Explanation:

The area of a trapezium can be calculated using the formula: A = ½ × (a + b) × h.

A = ½ × (a + b) × h.

A = ½ × (22 + 8) × 4.

A = 0.5 x 30 x 4

A = 60 sq ft

The area of a semicircle is half of the area of the circle. As the area of a circle is πr^{2}. So, the area of a semicircle is 1/2(πr^{2} ), where r is the radius.

d = 8 ft

r = d/2 = 8/2 = 4 ft

A = 1/2(πr^{2})

A = 0.5 x 3.14 x 4 x 4

A = 12.56 sq ft

Area of patio is = area of trapezium + area of semi circle

A = 60 + 12.56

A = 72.56 sq ft

Question 3.

**Open-Ended** Juanita is making a ribbon as shown.

Explain two different ways you can find the area of the ribbon. Then find the area of the ribbon.

Answer:

39 sq cm

Explanation:

Two ways is as follows

First method:

first calculate the are of figure B

A1 = length x width

A1 = 11 x 3 = 33 sq cm

area of a triangle of figure A

A = (1/2) x base x height

A = 0.5 x 1.5 x 4 = 3 sq cm

two such triangle 3 + 3 = 6sq cm

Total are of a given ribbon is = 33 + 6 = 39 sq cm

Second way of finding the area of ribbon is

first calculate the are of figure A

A1 = length x width

A1 = 15 x 3 = 45 sq cm

area of a triangle of figure B

A = (1/2) x base x height

A = 0.5 x 3 x 4 = 6 sq cm

Total are of a given ribbon is = 45 – 6 = 39 sq cm

**For Problems 4-5, find the area of the composite figure. Use 3.14 for π.**

Question 4.

Answer:

23 sq units

Explanation:

the area of the composite figure

20 sq units + 6×0.5 sq units

20 + 3 = 23 sq units

Question 5.

Answer:

857 sq ft

Explanation:

Area of figure A

d = 20 ft

r = 10 ft

Area of a semi circle = 1/2 (3.14 x 10 x 10)

Area of semi circle = 157 sq ft

Area of figure B

A = (1/2) x base x height

A = 0.5 x 20 x 60 = 600 sq ft

Area of figure C

A3 = length x width

A3 = 50 x 20 = 100 sq ft

Total area A = A1 +A2 + A3

A = 157 + 600 + 100 = 857 sq ft

**Test Prep**

Question 6.

A plot of grass behind a building is shown. What is the area of the plot of grass?

Answer:

Area = 164 sq m

Explanation:

the area of the plot of grass is

A = A1 + A2 + A3

A1 = length x width

A1 = 8 x 16

A1 = 128 sq m

A2 = length x width

A2 = 8 x 4

A2 = 32 sq m

A3 =(1/2) base x height

A3 = 0.5 x 2 x 4

A3 = 4 sq m

the area of the plot of grass is

A = A1 + A2 + A3

A = 128 + 32 + 4 = 164 sq m

Question 7.

Eric is designing a logo for a company. The logo consists of two identical parallelograms joined at their longest sides. One of the parallelograms has a base of 2.5 centimeters and a height of 1.25 centimeters. What is the area of the logo?

Answer:

6.25 sq cm

Explanation:

parallelograms has a base of 2.5 centimeters and a height of 1.25 centimeters.

Area = base x height

Area = 2.5 x 1.25 = 3.125 sq cm

the area of the logo

3.125 sq cm + 3.125 sq cm = 6.25 sq cm

Question 8.

Find the approximate area of the composite figure. Use 3.14 for π.

(A) 174.96 cm^{2}

(B) 231.48 cm^{2}

(C) 288 cm^{2}

(D) 344.52 cm^{2}

Answer:

Option (B)

Explanation:

base of triangle = 6 cm

height of triangle = 12 cm

base of rectangle = 21 cm

**Spiral Review**

Question 9.

How many unique triangles can be made with sides of lengths 4 cm, 7 cm, and 12 cm: none, one, or many?

Answer:

Only one unique triangle can be made with a given lengths as shown below.

Explanation:

Triangle has 3 sides

Question 10.

A cylindrical garbage can has the dimensions shown.

A. What is the area of a horizontal cross-section of the cylinder? Use 3.14 for π.

Answer:

Area = 113.04 sq in

Explanation:

d = 12 in

r = d/2

r = 12/2 in

r = 6 in

The area of a horizontal cross-section of the cylinder is circle

A = π. r x r

A = 3.14 x 6 x 6

A = 36 x 3.14

A = 113.04 sq in

B. What is the area of a vertical cross-section of the cylinder through the centers of the bases?

Answer:

Area = 180 sq in

Explanation:

Given, base = 12in

Length = 15 in

the area of a vertical cross-section of the cylinder is rectangle

A = length x width

A = 12 x 15

A = 180 sq in

C. Which cross-section has the greater area, and by how much?

Answer:

Area = 66.96 sq in

vertical cross section is greater then the horizontal cross section

Explanation:

A1 = 180 sq in vertical cross section

A 2= 113.04 sq in is horizontal cross section

A1 – A2 = 180 – 113.04 = 66.96 sq in