﻿ Perimeters and Areas of Compound Figures Worksheet | Problems & Solutions

# Perimeters and Areas of Compound Figures Worksheet

Perimeters and Areas of Compound Figures Worksheet
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1.
Find the perimeter of the shaded region in the figure, if X, Y, Z are the mid-points of the corresponding sides and XY = 4 m and XZ = 5 m.

 a. 17 m2 b. 18 m c. 19 m d. 17 m

#### Solution:

Perimeter of the shaded region in the figure = XY + YZ + ZX

Length of the side YZ = YO + OZ = 4 + 4 = 8 m
[Since CE = ED = 4 m, YO = OZ = 4 m.]

Perimeter of the shaded region = 4 + 8 + 5 = 17 m

2.
Find the perimeter of the figure.

 a. 32 ft b. 25 ft c. 31 ft d. 28 ft

#### Solution:

The perimeter of the figure = AB + BC + CD + DE + EF + FG + GH + HA .

From the figure, length of AB = length of EF = 2 ft

From the figure, length of BC = length of DE = 3 ft

From the figure, length of CD = 4 ft

From the figure, length of AH = length of FG = 5 ft

From the figure, length of GH = 7 ft

Perimeter of the figure = sum of the lengths of all the sides = 2 + 3 + 4 + 3 + 2 + 5 + 7 + 5 = 31 ft.

3.
What is the perimeter of the figure?

 a. 30 in. b. 22 cm c. 15 cm d. 30 cm

#### Solution:

The perimeter of the figure = sum of the perimeters of the triangles ABC and CDE.

= 4 + 6 + 5
Perimeter of the triangle ABC = sum of the lengths of the sides of the triangle ABC = AB + BC + CA
[Substitute the lengths of the sides.]

= 15 cm

= 5 + 4 + 6
Perimeter of the triangle CDE = sum of the lengths of the sides of the triangle CDE = CD + DE + EC
[Substitute the lengths.]

= 15 cm

Perimeter of the figure = 15 + 15 = 30 cm
[Substitute the perimeters of the triangles and add.]

4.
Find the perimeter of ABCD, if ABCE is a parallelogram and ADE is an equilateral triangle.

 a. 20 m b. 16 m c. 18 m d. 22 m

#### Solution:

Perimeter of ABCD = AB + BC + CE + ED + DA

Since ADE is an equilateral triangle, AD = DE = EA = 2 m

AB = EC = 6 m and BC = AE = 2 m
[Since ABCE is a parallelogram, AB = EC and BC = AE.]

Perimeter of the figure = 6 + 2 + 6 + 2 + 2 = 18 m

The perimeter of ABCD is 18 m.

5.
The dimensions of the rectangle are in cm. Find the combined area of the two rectangles.

 a. 24 cm2 b. 32 cm2 c. 40 cm2 d. 42 cm2

#### Solution:

Area of a rectangle = length x width

= (3 + 7) x 4
[Substitute length = (3 + 7) and width = 4.]

= 10 x 4
[Add the values inside the grouping symbols.]

= 40
[Multiply.]

So, the area of the rectangle is 40 cm2.

6.
Find the area of the unshaded region in the figure, if the parallelogram ABCD is divided into smaller parallelograms of equal size and the area of the shaded region is 36 in.2

 a. 108 in.2 b. 104 in.2 c. 114 in.2 d. 125 in.2

#### Solution:

The number of small parallelograms, which are shaded = 9

Area of each small parallelogram = (area of the shaded region) / (number of small parallelograms in the shaded region)

= 369 = 4 in.2
[Substitute the values.]

Number of small parallelograms, which are not shaded = 26

= 26 × 4 = 104 in.2
So, area of the region not shaded = number of small parallelograms not shaded × area of each small parallelogram
[Substitute the values.]

7.
What is the ratio of the shaded region to the unshaded region in the figure, if AF = FE = BD = 2 ft?

 a. 3 : 2 b. 2 : 3 c. 2 : 1 d. 1 : 2

#### Solution:

As AF = FE = BD, the bases of the three triangles ABF, BFD, and FDE are equal.

From the figure, the three triangles ABF, BFD, and FDE have equal heights.

The areas of all the three triangles are equal.
[Area of triangle = 1 / 2 × base × height]

So, 2 out of 3 equal parts are shaded and 1 part is not shaded.

The ratio of the shaded region to the unshaded region = 2 : 1

8.
ΔACE is formed by Blue, Green, Red, and Yellow colored isosceles triangles. What is the perimeter of ΔACE?

 a. 23 in. b. 28 in. c. 22 in. d. 31 in.

#### Solution:

Perimeter of ΔACE = AC + CE + EA

Measure of AC = AB + BC = 4 + 4 = 8 in.

Measure of CE = CD + DE = 4 + 4 = 8 in.

Measure of EA = AF + FE = 3 + 3 = 6 in.

The perimeter of the triangle ACE = 4 + 4 + 4 + 4 + 3 + 3 = 22 in.
[Substitute the values.]

So, perimeter of ΔACE is 22 in.

9.
The trapezoid ABDE is formed by joining the three equilateral triangles ABC, CDE, and ACE as shown. What is the perimeter of ABDE?

 a. 25 in. b. 15 in. c. 20 in. d. None of the above

#### Solution:

The perimeter of ABDE = AB + BC + CD + DE + EA

From the figure, AB = BC = CD = DE = AE = 4 in.
[Since, the measures of each side of all the triangles is equal to 4 in.]

= 20 in.
The perimeter of ABDE = 4 + 4 + 4 + 4 + 4
[Substitute the values.]

10.
What is the perimeter of the figure shown?

 a. 20 in. b. 24 in. c. 22 in. d. 18 in.

#### Solution:

The perimeter of the figure = sum of the lengths of all the sides = AF + FB + BE + EC + CD + DA

From the figure, the length of the side AF = 3 in.

From the figure, the length of the side FB = 3 in.

From the figure, the length of the side BE = 4 in.

From the figure, the length of the side EC = 4 in.

From the figure, the length of the side CD = 5 in.

From the figure, the length of the side DA = 5 in.

The perimeter of the figure = 3 + 3 + 4 + 4 + 5 + 5 = 24 in.