This document provides examples of calculating the area of a trapezoid using the formula Area = 1⁄2(b+B)h, where b and B are the two bases and h is the height. It demonstrates finding the height when it is not explicitly given by using properties of isosceles triangles or the Pythagorean theorem. In one example, it shows dividing the larger base into pieces to find the height of two congruent triangles formed. In another, it notes that if the base angles are 45 degrees, the triangles formed will be isosceles and the shared height can be used for the trapezoid area.

1. Area of a Trapezoid NCVPS Summer 2010

2. Area formulas for Unit 9

3. Trapezoid Area = ½ (B + b)(h)

4. Example 1 Find the area of the trapezoid: b = 15, B = 23 and h = 7 Area = ½(15 + 23) (7) = ½ (38)(7) = 19(7) = 133 square units

5. Example 2 We have both bases, 12 cm and 18 cm. But there is no perpendicular height! How do we find it?

6. Example 2 The trapezoid is isosceles! When we draw the perpendicular heights, we create two congruent triangles at either end. The base length of 18 is divided into 3 pieces – a segment of 12 cm, and two segments of 3 cm each.

7. Example 2 Use Pythagorean Theorem to find h! h2 + 32 = 52 h2 + 9 = 25 h2 = 16 h = sqrt(16) = 4 Area = ½ (12 + 18)(4) = ½ (30)(4) = 15(4) = 60 sq cm

8. Example 3 The perpendicular height is not given in this problem. The base angle of 45o means the other angle is also 45o. The triangle is isosceles! Then the height of the triangle is also 5 in. That gives us the height of the trapezoid! Area = ½ (9+ 11)(5) = ½ (20)(5) = 50 sq in