Area of Trapezoids

Given the formula for the area of a parallelogram we are going to use that information to discover the formula for the area of a trapezoid. Watch carefully not to miss it!

Notice that the trapezoid is half the area of the parallelogram. (b 1 + b 2 ) h Copy the trapezoid, flip it over, and put it next to the original. It makes a parallelogram. We are going to use the area of a parallelogram to find the area of a trapezoid. It takes two trapezoids to make one parallelogram.

(b 1 + b 2 ) h Parallelogram Trapezoid Notice that the trapezoid is half the area of the parallelogram. How do we find half the area ? A = (b 1 + b 2 ) h Hint: Think of area of a triangle.

Area of Trapezoid 2 in 6 in 3 in A = (b 1 + b 2 ) h 4 in A = (2 + 6) 3 A = (8) 3 A = 4 3 A = 12 in²

Area of Trapezoid 3 m 8 m 4 m 5 m A = (b 1 + b 2 ) h A = (3 + 8) 4 A = (11) 4 A = (44) A = 22 m²

4 in 5 in 7 in 6 in A = 24 in² 5 in 12 in 7 in A = 59.5 in²

Find the HEIGHT of the Trapezoid 7 ft 15 ft A = (b 1 + b 2 ) h 88 = (15 + 7) h 88 = (22) h 88 = 11 h h = 8 ft A = 88 ft² h

h = 12 m 2 Find the height of the trapezoid. 6.5 m 11.5 m A = 108 m² h

How would you find the unknown base? SOLUTION A = 1 2 h(b 1 + b 2 ) b 2 = 15 m 1 2 (8)(9 + b 2 ) 96 = 15 = b 2 96 = 4(9 + b 2 ) 24 = 9 + b 2

Practice: Area of Trapezoids Worksheet