2003 AMC 8 Problems/Problem 21
Problem
The area of trapezoid is . The altitude is 8 cm, is 10 cm, and is 17 cm. What is , in centimeters?
Solution
Using the formula for the area of a trapezoid, we have . Thus . Drop perpendiculars from to and from to and let them hit at and respectively. Note that each of these perpendiculars has length . From the Pythagorean Theorem, and thus . Substituting back into our original equation we have thus