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

Let us lower the height from the top of the obtuse angle C to the larger base AD.

By the property of an isosceles trapezoid, the height lowered from the top of an obtuse angle to the larger base divides it into two segments, the smaller of which is equal to the half-difference of the bases, and the larger half-sum of the bases.

DY = (AD – BC) / 2 = (18 – 8) / 2 = 10/2 = 5 cm.

From the right-angled triangle CНD, by the Pythagorean theorem, we determine the leg CH, which is the height of the trapezoid.

CH ^ 2 = СD ^ 2 – DН ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

CH = √144 = 12 cm.

Determine the area of ​​the trapezoid:

S = (BP + BC) * CH / 2 = (18 + 8) * 12/2 = 156 cm2.

Answer: The area of ​​the trapezoid is 156 cm2.