In an isosceles trapezoid, the base is 10 cm and the side is 24 cm 25 cm. Find the area of the trapezoid.

In an isosceles trapezoid, a = 10 cm is a smaller base, b = 24 cm is a larger base, c = 25 cm is a lateral side.
Knowing all sides of an isosceles trapezoid, its area can be found by the formula:
S = √ ((p – a) (p – b) ((p – c) ^ 2)),
where S is the area of an isosceles trapezoid, p is a semiperimeter.
p = (a + b + 2c) / 2;
p = (10 + 24 + 2 * 25) / 2 = 84/2 = 42 (cm).
S = √ ((42 – 10) (42 – 24) ((42 – 25) ^ 2)) = √ (32 * 18 * (17) ^ 2) = √ (32 * 18 * 289) = √166464 = 408 (cm square).
Answer: S = 408 cm square.