The 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.
Example 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 cm^{2}
Example 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 in^{2}
Example 3: The area of a parallelogram is 24 square centimeters and the base is 4 centimeters. Find the height.
Solution:
A = B * H
24 cm^{2} = (4 cm) · H
24 cm^{2} ÷ (4 cm) = H
H = 6 cm
Summary: 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. |
2. | Find the area of a parallelogram with a base of 4 meters and a height of 9 meters. |
3. | The area of a parallelogram is 64 square inches and the height is 16 inches. Find the base. |
4. | A parallelogram has an area of 54 square centimeters and a base of 6 centimeters. Find the height. |
5. | A parallelogram-shaped garden has an area of 42 square yards and a height of 6 yards. Find the base. |