# The bases of the trapezoid are 6 and 34, the area of the trapezoid is 300, and one of the sides is 25.

August 30, 2021 | education

| **The bases of the trapezoid are 6 and 34, the area of the trapezoid is 300, and one of the sides is 25. Find the second side of the trapezoid.**

Let us lower the height CH from the top of the trapezoid.

The area of the trapezoid is: S = (AD + BC) * CH / 2.

300 = (34 + 6) * CH / 2.

CH = 600/40 = 15 cm.

In the triangle СНD, we define, according to the Pythagorean theorem, the leg DH.

DH ^ 2 = CD ^ 2 – CH ^ 2 = 25 ^ 2 – 15 ^ 2 = 625 – 225 = 400.

DН = 20 cm.

Determine the length of the segment AK.

AK = AD – KH – DH = 34 – 6 – 20 = 8 cm.

In a right-angled triangle ABK, we determine the length of the hypotenuse AB.

AB ^ 2 = BK ^ 2 + AK ^ 2 = 15 ^ 2 + 8 ^ 2 = 225 + 64 = 289.

AB = 17 cm.

Answer: Lateral side AB = 17 cm.