Find the area of a trapezoid ABCD with bases AD and BC if AD = 12cm, BC = 6cm, CD = 5cm, AC = 13cm?

To solve this problem you need:
1) Draw trapezoid ABCD with bases AD and BC.
2) Draw the AC diagonal.
3) Now it is necessary to consider the ACD triangle.
By the Pythagorean theorem:
13 ^ 2 = 12 ^ 2 + 5 ^ 2
169 = 169 – right-angled triangle. => Right-angled trapezoid. ADC angle = 90 degrees.
4) the height is CD, and the bases are AD and BC.
5) Find the area of the trapezoid.
S = 1/2 * (AD + BC) * h
S = 1/2 * (AD + BC) * CD = 1/2 * (12 + 6) * 5 = 9 * 5 = 45 (cm ^ 2)
Answer. 45 cv ^ 2