Area of a Parallelogram

Area of a Parallelogram

parallelogramThe area of a polygon is the number of square units inside the polygon. Area is 2-dimensional like a carpet or an area rug.

A parallelogram is a 4-sided shape formed by two pairs of parallel lines. Opposite sides are equal in length and opposite angles are equal in measure. To find the area of a parallelogram, multiply the base by the height. The formula is:

A = B * H where B is the base, H is the height, and * means multiply.

The base and height of a parallelogram must be perpendicular. However, the lateral sides of a parallelogram are not perpendicular to the base. Thus, a dotted line is drawn to represent the height. Let's look at some examples involving the area of a parallelogram.


parallelogramExample 1: Find the area of a parallelogram with a base of 12 centimeters and a height of 5 centimeters.

Solution:

A = B * H

A = (12 cm) · (5 cm)

A = 60 cm2


parallelogramExample 2: Find the area of a parallelogram with a base of 7 inches and a height of 10 inches.

Solution:

A = B * H

A = (7 in) · (10 in)

A = 70 in2


parallelogramExample 3: The area of a parallelogram is 24 square centimeters and the base is 4 centimeters. Find the height.

Solution:

A = B * H

24 cm2 = (4 cm) · H

24 cm2 ÷ (4 cm) = H

H = 6 cm


parallelogramSummary: Given the base and height of a parallelogram, we can find the area. Given the area of a parallelogram and either the base or the height, we can find the missing dimension. The formula for area of a parallelogram is:

A = B * H where B is the base, H is the height, and * means multiply.


Exercises

Directions: Read each question below. Click once in an ANSWER BOX and type in your answer; then click ENTER. Your answers should be given as whole numbers greater than zero. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.

1. Find the area of a parallelogram with a base of 8 feet and a height of 3 feet. 
ANSWER BOX:  A =  ft2  

RESULTS BOX: 

2. Find the area of a parallelogram with a base of 4 meters and a height of 9 meters. 
ANSWER BOX:  A =  m2  

RESULTS BOX: 

3. The area of a parallelogram is 64 square inches and the height is 16 inches. Find the base. 
ANSWER BOX:  B =  in  

RESULTS BOX: 

4. A parallelogram has an area of 54 square centimeters and a base of 6 centimeters. Find the height. 
ANSWER BOX:  H =  cm  

RESULTS BOX: 

5. A parallelogram-shaped garden has an area of 42 square yards and a height of 6 yards. Find the base. 
ANSWER BOX:  B =  yd  

RESULTS BOX: