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.