Find the area of an isosceles trapezoid if its bases are 4 and 10 cm and the side is 5 cm.

Given:

isosceles trapezoid ABCE,

BC = 8 centimeters,

AE = 10 centimeters,

AB = CE = 5 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 = HC = 4 centimeters.

2. Right-angled triangle ABН = right-angled triangle COE along the hypotenuse and acute angle, since angle A = angle E and CE = AB. Then CE = AH = (10 – 4): 2 = 6: 2 = 3 (centimeters).

3. Consider a right-angled triangle BHA. By the Pythagorean theorem:

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 25 – 9;

BH ^ 2 = 16;

BH = 4 centimeters.

4. The area of ​​the trapezoid ABCE, that is, S ABCE = 1/2 * (BC + AE) * BH = 1/2 * (4 + 10) * 4 = 2 * 14 = 28 cm ^ 2.

Answer: 28 cm ^ 2.