# You are given a trapezoid ABCD with AD || BC (AD and BC are parallel bases). In this case, the size of the sides is AB

**You are given a trapezoid ABCD with AD || BC (AD and BC are parallel bases). In this case, the size of the sides is AB = 8 cm, BC = 7.5 cm, CD = 6 cm, AD = 17.5 cm Find the area of the trapezoid.**

Let us draw from the vertices B and C the heights of the trapezoid ВН and СK.

Let the segment AH = X cm, then DK = (17.5 – 7.5 – X) = 10 – X.

Then in the triangle ABN, by the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 64 – X ^ 2.

In the triangle CDK, by the Pythagorean theorem, CK ^ 2 = CD ^ 2 – DK ^ 2 = 36 – (10 – X) 2.

Since ВН = СK, then

64 – X ^ 2 = 36 – (10 – X) ^ 2.

64 – X ^ 2 = 36 – 100 + 20 * X – X ^ 2.

20 * X = 128.

X = AH = 6.4 cm.

Then BH ^ 2 = AB ^ 2 – AH ^ 2 = 64 – 40.96 = 23.04.

BH = 4.8 cm.

Determine the area of the trapezoid. Savsd = (ВС + АD) * ВН / 2 = (17.5 + 7.5) * 4.8 / 2 = 60 cm2.

Answer: The area of the trapezoid is 60 cm2.