In trapezoid ABCD, the base lengths are known: AD = 10, BC = 4, and its area is 126. Find the area of triangle ABC.

univerkov | August 15, 2021 | education

The solution of the problem:

1) The area of the trapezoid S = (a + b) * h / 2, where a = BC, b = AD, h = AH – the height lowered to BC.

Let us express the height: h = 2 * s / (a + b) = 2 * 126 / (10 + 4) = 18 = AH.

2) Area of triangle ABC = BC * AH * 0.5 = 4 * 18 * 0.5 = 36.

Answer: 36

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