The bases of an isosceles trapezoid are 15 and 25, and its sides are 13. Find the area of the trapezoid.

Given:
isosceles trapezium ABCD;
BC = 15;
AD = 25;
AB = CD = 13;
Find Savsd -?
Decision:
1) Let’s draw the heights BK and CM;
2) Right-angled triangles ABK = CMD as angle D = angle A, hypotenuse AB = CD.
3) The BKMS quadrangle is a rectangle. Then BC = KM. Therefore, AK = MD = (25 – 15) / 2 = 5 (cm);
4) Consider a right-angled triangle ABK. By the Pythagorean theorem:
BK = √ (AB ^ 2 – AK ^ 2);
BK = √ (169 – 25);
BK = √44;
BK = 2√11;
5) Savsd = (BC + AD) / 2 * BK;
Savsd = (15 + 25) / 2 * 2√11;
Savsd = 40√11 cm squared.
Answer: 40√11 centimeters squared.