# 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. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.