The bases of an isosceles trapezoid are 8 and 18, and its sides are 13. Find the area of the trapezoid.

An isosceles trapezoid is a quadrilateral, two sides (bases) of which are parallel and not equal to each other, and the other two sides (sides) are equal, the angles at the bases of an isosceles trapezoid are equal.
The area of ​​an isosceles trapezoid can be found knowing the lengths of all sides, using a formula that is similar to Heron’s formula for triangles:
S = (√ (a + b) ^ 2 (a – b + 2c) (b – a + 2c)) / 4,
where a is a larger base, b is a smaller base, c is a side.
Substitute the data known from the condition and find the area of ​​the trapezoid:
S = (√ (18 + 8) ^ 2 (18 – 8 + 2 * 13) (8 – 18 + 2 * 13)) / 4 = (√ (26 ^ 2 * 36 * 16)) / 4 = √ ( 676 * 36 * 16) / 4 = √389376 / 4 = 624/4 = 156.
Answer: S = 156.