In an isosceles trapezoid, the side is 13 cm, the base 10 cm and 20 cm. Find the area of the trapezoid.

Given:

isosceles trapezoid ABCE,

BC = 10 centimeters,

AE = 20 centimeters,

AB = CE = 13 centimeters.

Find the area of ​​the trapezoid ABCE, that is, S ABCE -?

Decision:

1. Consider an isosceles trapezoid ABCE. Let’s draw the heights of HВ and CO. We get the HBCO rectangle. He has ВН = CO and BC = HO = 10 centimeters.

2. Right-angled triangle ABН = right-angled triangle SOE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then OE = AH = (20 – 10): 2 = 10: 2 = 5 (centimeters).

3. Consider the BHA triangle. By the Pythagorean theorem: BH ^ 2 = AB ^ 2 – AH ^ 2 = 169 – 25 = 144, BH = 12 centimeters.

4. The area of ​​the trapezoid ABCE, that is, S ABCE = 1/2 * (BC + AE) * BH = 1/2 * (10 + 20) * 12 = 6 * 30 = 180 cm ^ 2.

Answer: 180 cm ^ 2.