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 cm^{2} each, as in the figure.

a. | 82 cm ^{2} | ||

b. | 78 cm ^{2} | ||

c. | 76 cm ^{2} | ||

d. | 80 cm ^{2} |

The parallelogram ABCD consists of 8 trapezoids.

The area of the parallelogram ABCD = 10 × 8 = 80 cm

Correct answer : (4)

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} |

= 10 × 7

[Substitute the values of base and height.]

Area of the parallelogram = 70 in.

Correct answer : (3)

3.

What is the area of the parallelogram?

a. | 945 yd ^{2} | ||

b. | 525 yd ^{2} | ||

c. | 745 yd ^{2} | ||

d. | 100 yd ^{2} |

= 45 × 21 = 945 yd

[Simplify.]

Correct answer : (1)

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 |

Let

Area of the parallelogram =

[Since base length = height.]

The base length of the parallelogram is 8 ft.

Correct answer : (1)

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} |

Let

The side of the square = 4 in.

[

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.

Correct answer : (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} |

Height of the parallelogram = 10 in.

Area of the parallelogram A = base x height

A = 22 x 10 = 220 in.

[Substitute height = 10 and base = 22.]

The area of the parallelogram is 220 in.

Correct answer : (1)

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 |

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.

Correct answer : (3)

8.

What is the area of a parallelogram, if its base is 3 m and height is 5 m?

a. | 13 m ^{2} | ||

b. | 15 m ^{2} | ||

c. | 17 m ^{2} | ||

d. | None of the above |

[Formula.]

= 3 x 5

[Substitute the values of base and height.]

= 15

[Multiply.]

So, area of the parallelogram is 15 m

Correct answer : (2)

9.

Find the area of the colored region in the figure.

a. | 26 cm ^{2} | ||

b. | 22 cm ^{2} | ||

c. | 28 cm ^{2} | ||

d. | 20 cm ^{2} |

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 cm

Correct answer : (3)

10.

What is the area of a parallelogram, if its base is 3 ft and height is 5 ft?

a. | 17 ft ^{2} | ||

b. | 13 ft ^{2} | ||

c. | 15 ft ^{2} | ||

d. | None of the above |

[Formula.]

= 3 x 5

[Substitute the values of base and height.]

= 15

[Multiply.]

So, area of the parallelogram is 15 ft

Correct answer : (3)