Area of a Trapezoid

Watch carefully not to miss it! Area of a Trapezoid Given the formula for area of a triangle and the formula for 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!

This trapezoid is regular. Area of a Trapezoid This trapezoid is regular. regular trapezoid Also known as an isosceles trapezoid This trapezoid is an irregular trapezoid. irregular trapezoid

Copy that trapezoid, flip it over, and put it next to the original Area of a Trapezoid b2 b1 h b1 What polygon is it now? h h Parallelogram b2 (b1 + b2) Give the height, base 1 & base 2 Copy that trapezoid, flip it over, and put it next to the original

Area of a Trapezoid h (b1 + b2) put together with a similar flipped trapezoid, we found it made a parallelogram. Given our original trapezoid h (b1 + b2) We are going to use the area of a parallelogram to find the area of a trapezoid. Notice that the trapezoid is half the area of the parallelogram. It takes two trapezoids to make one parallelogram.

Trapezoid Parallelogram Area of a Trapezoid h (b1 + b2) Notice that the trapezoid is half the area of the parallelogram. How do we find half the area? h Hint: Think of area of a triangle. (b1 + b2) Trapezoid Parallelogram A = (b1 + b2) • h 2

Area of Trapezoid Area of a Trapezoid 2 in 4 in A = (b1 + b2) • h 3 in

Area of Trapezoid Area of a Trapezoid 3 m 5 m A = (b1 + b2) • h 4 m 2

Area of a Trapezoid 5 in 4 in 6 in 7 in Here is another way to look at the trapezoid formula. Instead of dividing by 2, multiply by ½

Area of a Trapezoid Practice

Area of a Trapezoid A = (b1 + b2) x h A = (4 + 5) x 3 2 A = (9) x 3 27 4 ft A = (base1 + base2) x height 3 ft 2 A = (b1 + b2) x h 5 ft 2 A = (4 + 5) x 3 2 A = (9) x 3 27 = = 13.5 ft2 2 2

Area of Polygons The Area of a figure is the number of square units needed to cover it. Rectangle Parallelogram Triangle 7 4 8 7 5 5 10 8