# Calculate the area of an isosceles trapezoid, the bases of which are equal to 8 cm and 10 cm

**Calculate the area of an isosceles trapezoid, the bases of which are equal to 8 cm and 10 cm, if it is known that the center of the circle described around the trapezoid is on a larger base.**

Given: ABCD – isosceles trapezoid,

AD = 10 cm,

BC = 8 cm,

O belongs to the foundation AD.

Find S avsd -?

Solution:

1) Let’s draw the heights BK and CM. Triangles ABK = CMD as SD = AB and angle A = angle D;

2) AK = MD = (AD – BC) / 2 = (10 – 8) / 2 = 2/2 = 1 (cm);

3) KO = AO – AK, AO = AD / 2 = 10/2 = 5 (cm). Then

KO = 5 – 1 = 4 (cm);

4) Consider a right-angled triangle KBO.

By the Pythagorean theorem, BK ^ 2 = BO ^ 2 – KO ^ 2,

BK ^ 2 = 25 – 16,

BK ^ 2 = 9,

BK = 3 cm;

5) S avsd = (BC + AD) / 2 * VK,

S avsd = (8 + 10) / 2 * 3,

S aws = 27 square centimeters.

Answer: 27 square centimeters.