Lesson 1: Areas of Parallelograms

Property

A parallelogram can be rearranged into a rectangle with the same base and height. Choose any side of the parallelogram as the base (length $b$), and let $h$ be the perpendicular distance between the base and the opposite side.
The area is given by the formula:

Examples

• A parallelogram has a base of 12 cm and a height of 5 cm. Its area is $12 \times 5 = 60$ square cm.
• A section of a patio is shaped like a parallelogram with a base of 8 feet and a height of 6 feet. The area is $8 \times 6 = 48$ square feet.
• Even if the slanted side is 9 inches, if the base is 15 inches and the height is 7 inches, the area is $15 \times 7 = 105$ square inches.

Explanation

Think of a parallelogram as a slanted rectangle. By slicing off a triangle from one end and moving it to the other, you create a perfect rectangle. This new rectangle has the same base and height, which is why the area formula works!

Property

The height of a parallelogram is the perpendicular distance between parallel sides, not the length of the slanted side. Height is always measured at a $90°$ angle to the base.

Examples

Property

When a parallelogram is drawn on a coordinate plane with horizontal and vertical sides, we can use the coordinates to measure the base and height, then apply the parallelogram area formula.

Parallelogram Area: $A = \text{base} \times \text{height}$