Find the area of an isosceles trapezoid if its smaller base is 7 cm, the lateral side is 13 cm, and the height is 12 cm.

Given:

isosceles trapezoid ABCE,

BC = 7 centimeters,

AB = CE = 13 centimeters,

BH = 12 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 the HВ and CO. We get the HBCO rectangle. He has ВН = CO and BC = HO = 7 centimeters.

2. Consider a right-angled triangle ABН. By the Pythagorean theorem:

AH ^ 2 = AB ^ 2 – BH ^ 2;

AH ^ 2 = 169 – 144;

AH ^ 2 = 25;

AH = 5 centimeters.

3. Right-angled triangle ABН = right-angled triangle COE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then OE = AH = 5 (centimeters). Then AE = 5 + 5 + 7 = 17 (centimeters).

4. The area of ​​the trapezoid ABCE, that is, S ABCE = 1/2 * (BC + AE) * BH = 1/2 * (7 + 17) * 12 = 6 * 24 = 144 cm ^ 2.

Answer: 144 cm ^ 2.