The parallel sides of the trapezoid are 60 cm and 20 cm, and the sides are 13 cm and 37 cm. Find the area of the trapezoid.

Let’s build the heights BH and CK.

Quadrangle BCKN is a rectangle, then BH = CK, НK = BC = 20 cm.

АН + DК = АD – НК = 60 – 20 = 40 cm.

Let AH = X cm, then DK = 40 – X cm.

In a right-angled triangle ABH, by the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2.

In a right-angled triangle CDK, by the Pythagorean theorem, CK ^ 2 = CD ^ 2 – DK ^ 2.

AB ^ 2 – AH ^ 2 = CD ^ 2 – DK ^ 2.

169 – X ^ 2 = 1369 – 1600 + 80 * X – X ^ 2.

80 * X = 400.

X = 5 cm.

Then BH ^ 2 = 169 – 25 = 144.

BH = 12 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * BH / 2 = (20 + 60) * 12/2 = 480 cm2.

Answer: The area of the trapezoid is 480 cm2.