﻿ Perimeter of Irregular Shapes Worksheet | Problems & Solutions

# Perimeter of Irregular Shapes Worksheet

Perimeter of Irregular Shapes Worksheet
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1.
Estimate the area of the shaded region in the following figure.

 a. 185 square units b. 205 square units c. 145 square units d. 200 square units

#### Solution:

Number of squares that are filled = 37

Number of squares that are half filled = 8

Total number of squares filled = 37 + (8 × 1 / 2 ) = 41

Area of the figure = total number of squares filled × area of each square

= 41 × 5 = 205

So, the area of the figure is 205 square units.

2.
Estimate the area of the shaded region in the figure shown.

 a. 134 square units b. 120 square units c. 140 square units d. 130 square units

#### Solution:

Number of squares that are completely filled = 10

Number of squares that are half filled = 6

Total number of squares filled = 10 + (6 × 1 / 2 ) = 13

Area of the figure = Total number of squares filled × Area of each square

= 13 × 10 = 130

So, the area of the figure is 130 square units.

3.
Estimate the area of the shaded region in the figure, if each square is of 3 sq.cm.

 a. 154 sq.cm. b. 162 sq.cm. c. 136 sq.cm. d. 148 sq.cm.

#### Solution:

Number of squares that are filled = 48

Number of squares that are half filled = 12

Total number of squares filled = 48 + (12 × 1 / 2 ) = 54

Area of the figure = total number of squares filled × area of each square

= 54 × 3 = 162

So, the area of the figure is 162 sq.cm.

4.
Estimate the area of the shaded region of the figure, if each square measures 2 square inches.

 a. 60 square inches b. 50 square inches c. 70 square inches d. 40 square inches

#### Solution:

Number of squares that are filled = 20

Number of squares that are half filled = 10

Total number of squares filled = 20 + (10 × 1 / 2 ) = 25

Area of the figure = total number of squares filled × area of each square

= 25 × 2 = 50

So, the area of the figure is 50 square inches.

5.
Estimate the area of the shaded region of the following figure.

 a. 100 sq. units b. 28 sq. units c. 112 sq. units d. 120 sq. units

#### Solution:

Number of squares that are filled = 28

Area of the figure = total number of squares filled × area of each square

= 28 × 4 = 112

So, the area of the figure is 112 sq. units.

6.
Estimate the area of the figure if the area of each square is 4 mm2.

 a. 9 mm2 b. 18 mm2 c. 13 mm2 d. 52 mm2

#### Solution:

Number of squares that are completely filled = 4

Number of squares that are almost filled = 4

Number of squares that are about half filled = 10

Number of squares covering the figure = 4 + 4 + (10 × 1 / 2 )

= 4 + 4 + 5 = 13

Area of the figure = Number of squares × Area of each square

= 13 × 4 mm2 = 52 mm2
[Multiply.]

So, the area of the figure is about 52 mm2.

7.
About how many square units does the figure occupy, if each square covers an area of 5 square units?

 a. 80 square units b. 22 square units c. 16 square units d. 8 square units

#### Solution:

Number of squares that are completely filled = 8

Number of squares that are almost filled = 2

Number of squares that are about half filled = 12

Number of squares occupied by the figure = 8 + 2 + (12 × 1 / 2 )

= 8 + 2 + 6 = 16

Number of square units occupied by the figure = Number of squares occupied by the figure × Area of each square

= 16 × 5 square units = 80
[Multiply.]

So, the figure occupies about 80 square units.

8.
Estimate the area covered by the figure, if the area of each square is 3 cm2.

 a. 11 cm2 b. 36 cm2 c. 14 cm2 d. 42 cm2

#### Solution:

Number of squares that are completely filled = 4

Number of squares that are almost filled = 4

Number of squares that are about half filled = 8

Number of squares covered by the figure = 4 + 4 + (8 × 1 / 2 )

= 4 + 4 + 4 = 12

Area of the figure = Number of squares × Area of each square

= 12 × 3 cm2
[Multiply.]

So, the area covered by the figure is about 36 cm2.

9.
Each square in the figure covers an area of 2 in.2. What is the area of the figure shown?

 a. 42 in.2 b. 48 in.2 c. 24 in.2 d. 20 in.2

#### Solution:

Number of squares that are completely filled = 8

Number of squares that are almost filled = 8

Number of squares that are about half filled = 10

Number of squares occupied by the figure = 8 + 8 + (10 × 1 / 2 )

= 8 + 8 + 5 = 21 in.2

Area of the figure = Number of squares covered by the figure × Area of each square

= 21 × 2 in.2 = 42 in.2
[Multiply.]

So, the area of the figure shown is about 42 in.2.

10.
Calculate the approximate area of the figure if the area of each square is 6 square units.

 a. 270 square units b. 45 square units c. 260 square units d. 288 square units

#### Solution:

Number of squares that are completely filled = 30

Number of squares that are almost filled = 12

Number of squares that are about half filled = 6

Number of squares occupied by the figure = 30 + 12 + (6 × 1 / 2 )

= 30 + 12 + 3 = 45