# Math Help - Area of a Trapazoid...

1. ## Area of a Trapazoid...

Please look at the attached. The problem number I have to do is number 20. I believe the answer is 222. I

Here is my math: 15/2 times 20 = 150

12/2 times 12 = 72

150 + 72 = 222

Yes?

2. Hello, zachcumer!

Code:
D *  *  *  *  *  *  * C
*              *   *
*           *       *
12 *        * 20        * 15
*     *               *
*  *                   *
A *   *   *   *   *   *   * B
Area of a trapezoid: . $A \;=\;\frac{h}{2}(b_1 + b_2)$

We know that: $h = AD = 12$
. . But what are $b_1 = CD\text{ and }b_2 = AB$ ?

In right triangle $CDA\!:\;\;CD^2 + AD^2 \:=\:AC^2\quad\Rightarrow\quad CD^2 + 12^2 \:=\:20^2$
. . $CD^2 \:=\:256\quad\Rightarrow\quad \boxed{CD = 16}$

In right triangle $ACB\!:\;\;AB^2 \:=\:AC^2 + BC^2\quad\Rightarrow\quad AB^2 \:=\:20^2 + 15^2$
. . $AB^2 \:=\:625\quad\Rightarrow\quad \boxed{AB \:=\:25}$

Therefore: . $A \;=\;\frac{12}{2}(16 + 25) \;=\;246$