1. Lesson 11-3 Areas of Trapezoids (page 435) Essential Question How can you calculate the area of any figure?

2. Areas of Trapezoids

3. In a trapezoid, the bases are the parallel sides. b1b1 ➤ ➤ b2b2

4. The altitude of a trapezoid is any segment perpendicular to the line containing one base from a point on the opposite base. b2b2 b1b1 ➤ ➤ h

5. In a trapezoid, all altitudes have the same length, called the height (h). b2b2 b1b1 ➤ ➤ hhh

6. The area of a trapezoid equals half the product of the height and the sum of the bases. Theorem 11-5 b1b1 ➤ ➤ h A = ½ h(b 1 +b 2 ) b2b2

7. Here is an easy way to see why this works. You can justify the area formula for trapezoids by duplicating the trapezoid to form a parallelogram. b1b1 h b2b2

8. This is the justification for the theorem. The area of a trapezoid is equal to half the area of this parallelogram. b1b1 h b2b2 b1b1 h b2b2

9. A = ½ h(b 1 +b 2 ) The area of a trapezoid is equal to half the area of this parallelogram. b1b1 h b2b2 b1b1 h b2b2

10. The median of a trapezoid is the segment connecting the midpoints of the legs. Trapezoid Review b2b2 b1b1 ➤ ➤ median

11. median = ½ (b 1 +b 2 ) Trapezoid Review b2b2 b1b1 ➤ ➤ median

12. Trapezoid Formula #2 b2b2 b1b1 ➤ ➤ median Area = height  median = h  m

13. Example #1 Find the area of the trapezoid. 5 3 15

14. #2 Find the area of the trapezoid. 11 8 h x 60º = 4 30º b 1 = 11 b 2 = 15

15. #3 Find the length of the median and area of the trapezoid that has bases 18 & 24 and height 16. 18 24 16

16. #4 If the area of the trapezoid is 128 u 2 and its bases are 12 & 20, then find the height. 12 20 h

17. Assignment Written Exercises on pages 436 & 437 REQUIRED: 5 to 23 odd numbers * Bonus: #30 * How can you calculate the area of any figure? UPDATE YOUR STUDENT AID CARD!