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# Area of a trapezoid

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How to find perpendicular heights of trapezoids and find the area.

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### Area of a trapezoid

1. 1. Area of a Trapezoid<br />NCVPS<br />Summer 2010<br />
2. 2. Area formulas for Unit 9<br />
3. 3. Trapezoid Area = ½ (B + b)(h)<br />
4. 4. Example 1<br />Find the area of the trapezoid:<br />b = 15, B = 23 and h = 7<br />Area = ½(15 + 23) (7)<br /> = ½ (38)(7)<br /> = 19(7) <br /> = 133 square units<br />
5. 5. Example 2<br />We have both bases, 12 cm and 18 cm.<br />But there is no perpendicular height!<br />How do we find it?<br />
6. 6. Example 2<br />The trapezoid is isosceles!<br />When we draw the perpendicular heights, we create two congruent triangles at either end. <br />The base length of 18 is divided into 3 pieces – a segment of 12 cm, and two segments of 3 cm each.<br />
7. 7. Example 2<br />Use Pythagorean Theorem to find h!<br />h2 + 32 = 52<br />h2 + 9 = 25<br />h2 = 16<br />h = sqrt(16) = 4<br />Area = ½ (12 + 18)(4)<br /> = ½ (30)(4)<br /> = 15(4) = 60 sq cm<br />
8. 8. Example 3<br />The perpendicular height is not given in this problem. <br />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!<br />Area = ½ (9+ 11)(5) <br /> = ½ (20)(5) = 50 sq in<br />