Lesson 3: Areas of Trapezoids

Property

The area of a trapezoid can be found by splitting it into two triangles. Let the lengths of the two parallel sides (the bases) be $a$ and $b$, and let the perpendicular distance between them be the height, $h$. The area is the sum of the areas of the two triangles:

Examples

• A trapezoid has parallel bases of 6 inches and 10 inches, and a height of 5 inches. Its area is $\frac{1}{2}(6 + 10) \times 5 = 40$ square inches.
• A garden plot is a trapezoid with parallel sides of 8 ft and 12 ft. The height is 7 ft. The area is $\frac{1}{2}(8 + 12) \times 7 = 70$ square feet.
• A window is shaped like a trapezoid with bases of 20 cm and 30 cm and a height of 15 cm. Its area is $\frac{1}{2}(20 + 30) \times 15 = 375$ square cm.

Explanation

To find a trapezoid's area, you can average its two parallel bases and multiply by the height. This works because you can slice a trapezoid into two triangles, and this formula is just a shortcut for adding their areas together.

Property

When a trapezoid is drawn on a coordinate plane with horizontal parallel bases, we can use the coordinates to measure the lengths of the parallel bases and the height, then apply the trapezoid area formula.

Trapezoid Area: $A = \frac{1}{2}(b_1 + b_2) \cdot h$