﻿ Parallelogram Area Worksheet | Problems & Solutions

# Parallelogram Area Worksheet

Parallelogram Area Worksheet
• Page 1
1.
Find the area of the parallelogram ABCD, if it is constructed by red and blue color trapezoids of area 10 cm2 each, as in the figure.

 a. 82 cm2 b. 78 cm2 c. 76 cm2 d. 80 cm2

#### Solution:

The area of blue and red color trapezoids is 10 cm2 each.

The parallelogram ABCD consists of 8 trapezoids.

The area of the parallelogram ABCD = 10 × 8 = 80 cm2.

2.
Find the area of a parallelogram with a height of 7 inches and base measuring 10 inches.
 a. 71 in.2 b. 73 in.2 c. 70 in.2 d. 69 in.2

#### Solution:

Area of a parallelogram = base × height

= 10 × 7
[Substitute the values of base and height.]

Area of the parallelogram = 70 in.2

3.
What is the area of the parallelogram?

 a. 945 yd2 b. 525 yd2 c. 745 yd2 d. 100 yd2

#### Solution:

Area of the parallelogram = base × corresponding height

= 45 × 21 = 945 yd2
[Simplify.]

4.
The base length AB is equal to the corresponding height in a parallelogram ABCD. What is the base length AB, if the area of the parallelogram is 64 square feet?
 a. 8 ft b. 12 ft c. 6 ft d. 10 ft

#### Solution:

The area of the parallelogram = base length x height

Let x be the measure of the base.

Area of the parallelogram = x x x = x2 = 64
[Since base length = height.]

x = 8 ft

The base length of the parallelogram is 8 ft.

5.
DCFE is a square with an area 16 in.2 What is the area of the parallelogram ABCD, if AG measures 7 in.?

 a. 6 in.2 b. 12 in.2 c. 15 in.2 d. 24 in.2

#### Solution:

The area of the square = 16 in.2

Let x be the measure of the side of the square.

The side of the square = 4 in.
[x2 = 16, x = 4]

The length of the perpendicular AG = 7 in.

The height of the parallelogram = AG - CF = 7 - 4 = 3 in.

The base of the parallelogram DC = 4 in.

= 4 × 3
The area of the parallelogram ABCD = base × height

= 12 in.2

6.
One side of a parallelogram is 22 in. and its distance from the opposite side is 10 in. What is the area of the parallelogram?
 a. 220 in.2 b. 230 in.2 c. 227 in.2 d. 215 in.2

#### Solution:

The base of the parallelogram = 22 in.

Height of the parallelogram = 10 in.

Area of the parallelogram A = base x height

A = 22 x 10 = 220 in.2
[Substitute height = 10 and base = 22.]

The area of the parallelogram is 220 in.2

7.
Which of the following statements is true from the figure?

 a. Area of the parallelogram ABCD > area of the parallelogram PQRS b. Area of the parallelogram ABCD < area of the parallelogram PQRS c. Area of the parallelogram ABCD = area of the parallelogram PQRS. d. None of the above

#### Solution:

ABCD and PQRS are two parallelograms drawn on the dot graph.

Let the distance between two consecutive dots in the figure be 1 unit.

So, the base and height of the parallelogram ABCD are 2 units each.

= 2 x 2 = 4 square units
The area of the parallelogram ABCD = base x height
[Substitute base = height = 2 units.]

The base and height of the parallelogram PQRS are 4 units and 1 unit respectively.

= 4 square units
The area of the parallelogram PQRS = 4 x 1

So, area of the parallelogram ABCD is equal to the area of the parallelogram PQRS.

8.
What is the area of a parallelogram, if its base is 3 m and height is 5 m?
 a. 13 m2 b. 15 m2 c. 17 m2 d. None of the above

#### Solution:

Area of a parallelogram = base x height
[Formula.]

= 3 x 5
[Substitute the values of base and height.]

= 15
[Multiply.]

So, area of the parallelogram is 15 m2.

9.
Find the area of the colored region in the figure.

 a. 26 cm2 b. 22 cm2 c. 28 cm2 d. 20 cm2

#### Solution:

From the figure, the colored region is a parallelogram BEDF.

The base length of the parallelogram BEDF = 7 cm
[From the figure.]

The height of the parallelogram BEDF = 4 cm
[From the figure.]

Area of the parallelogram BEDF = base x height
[Formula.]

= 7 x 4
[Substitute the values.]

= 28

So, area of the colored region = area of the parallelogram BEDF = 28 cm2.

10.
What is the area of a parallelogram, if its base is 3 ft and height is 5 ft?
 a. 17 ft2 b. 13 ft2 c. 15 ft2 d. None of the above

#### Solution:

Area of a parallelogram = base x height
[Formula.]

= 3 x 5
[Substitute the values of base and height.]

= 15
[Multiply.]

So, area of the parallelogram is 15 ft2.