[jahxx3]

Im trying to find the area of a trapezoid. It only gives two lengths which are 20 cm and 36 cm. The two angles that are shown 45 degrees. But it does not give me the height. I need the steps and the answer for this question please!

[jcaron2]

Your description is a little ambiguous, but I'm going to assume that the two lengths (20 and 36) are the top and bottom, respectively, and the two sides are both leaning inward at 45° angles.

Since both sides lean in at 45° angles, you know that for every 1 cm of height each side comes in by 1 cm, meaning that the width of the top decreases by a total of 2 cm. Thus, starting with a base of 36 cm, if the trapezoid was only 1 cm tall, the top would be 34 cm wide. If it was 2 cm tall, the top would be 32 cm wide. In other words, t = b - 2*h, where t is the length of the top, b is the length of the bottom, and h is the height.

Plugging in your values of 36 and 20 for b and t, we can solve this to find h = 8 cm. Therefore, the area is 1/2 * (b+t) * h = 1/2 * (36 + 20) * 8 = 224 cm^2.