Area of a Trapezoid

Today we are going to review Area of a Triangle & Parallelogram. Then we are going to discover the Area of a Trapezoid.

Watch carefully not to miss it! Area of a Triangle Given the formula for area of a rectangle, we are going to use that information to discover the formula for the area of a triangle. Watch carefully not to miss it!

Area of a Triangle Given a right triangle Make a similar triangle,

Given a right triangle Make a similar triangle, Area of a Triangle Given a right triangle What polygon is this? A Rectangle Make a similar triangle, and put both triangles next to each other flip it

We can use the formula for area of a rectangle Area of a Triangle We can use the formula for area of a rectangle to find the formula for area of a triangle. Two triangles make one rectangle. We want to find half of the area of the rectangle. height h base b What is the formula for the area of a triangle?

This holds true for any triangle Area of a Triangle This holds true for any triangle height h base

Area of a Triangle A triangle is half the area of a rectangle. To find the area of a triangle, you use the rectangle formula (base times height) and divide it in half. A = base • height 2 13 m 12 m 5 m A = 5 • 12 = 30 m2 2

Area of a Triangle Area Perimeter Find the perimeter and area of this triangle. 5 cm 8 cm Area 3 cm 11 cm Perimeter P = a + b + c P = 5 + 8 + 11 P = 24 cm

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

Take out your study guide! Area of a Trapezoid The End! Take out your study guide!

Area of a Trapezoid A = (b1 + b2) x h A = (4 + 5) x 3 2 A = (9) x 3 27 # 5 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 #6 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