Lesson on Area of Trapezoids

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

A trapezoid is a 4-sided figure with one pair of parallel sides. For example, in the diagram to the right, the bases are parallel. To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:

or

where

is

,

is

,

is the height.

and · means multiply.

Each base of a trapezoid must be perpendicular to the height. In the diagram above, both bases are sides of the trapezoid. However, since the lateral sides are not perpendicular to either of the bases, a dotted line is drawn to represent the height.

In Examples 1 and 3 below, the height is a side of the trapezoid since it is perpendicular to the base. In Example 2, the lateral sides are not perpendicular to the base, so a dotted line is drawn to represent the height.

Example 1:	Find the area of a trapezoid with bases of 10 inches and 14 inches, and a height of 5 inches.
Solution:
	=  · (10 in + 14 in) · 5 in
	=  · (24 in) · (5 in)
	=  · 120 in^2
	A = 60 in^2

Example 2:

Find the area of a trapezoid with bases of 9 centimeters and 7 centimeters, and a height of 3 centimeters.

Solution:

=  · (9 cm + 7 cm) · 3 cm

=  · (16 cm) · (3 cm)

=  · 48 cm²

= 24 cm²

Example 3:

The area of a trapezoid is 52 square inches and the bases are 11 inches and 15 inches. Find the height.

Solution:

52 in² =   · (11 in + 15 in) ·

52 in² =   · (26 in) ·

52 in² = (13 in) ·

52 in² ÷ (13 in) =

= 4 in

Summary:

To find the area of a trapezoid, take the sum of its bases, multiply the sum by the height of the trapezoid, and then divide the result by 2, The formula for the area of a trapezoid is:

or

where

is

,

is

,  and

is the height.