Find the area of an isosceles trapezoid if its bases are 5 cm and 17 cm, and the side is 10 cm.

By the problem statement, we know all sides of the trapezoid. We calculate the area of a triangle of an isosceles trapezoid, where the sides are 10cm, the lower base is 17cm, and the upper 5cm. We use the formula
S = (a + b) / 2 * (c ^ 2 – ((a-b) ^ 2) / 4) ^ 1/2, where a is the lower base, b is the upper base, c are equal sides.
Substituting the values into the formula, we get:
S = (5 + 17) / 2 * (10 ^ 2 – ((17-5) ^ 2) / 4) ^ 1/2 = 11 + (100 – 144/4) ^ 1/2 = 11 + 64 ^ 1/2 = 1 + 8 = 9 (cm2).