The bases of an isosceles trapezoid are 5 and 17, and its sides are 10. Find the area of the trapezoid.

Let ABCD be a given trapezoid, AB = CD = 10. AD = 17, BC = 5.

The area of the trapezoid is calculated by the formula S = (a + b) / 2 * h, where a and b are the base of the trapezoid, h is the height of the trapezoid. The bases of the trapezoid are known, it remains to find the height.

Let’s omit the two heights BH and CE. HЕ will be equal to ВС = 5.

AH = ED = (17 – 5): 2 = 12: 2 = 6.

Triangle CED – rectangular (CE – height), according to the Pythagorean theorem CE ^ 2 = CD ^ 2 – DE ^ 2.

CE ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64.

CE = √64 = 8.

CE – height, now you can find the area of the trapezoid:

S = (17 + 5) / 2 * 8 = 22/2 * 8 = 11 * 8 = 88.

Answer: the area of the trapezoid is 88.