# In a trapezoid ABCD, AD = 4, BC = 1 and its area is 35 Nights, area ABC?

August 30, 2021 | education

| Let’s build the height of the HВ trapezoid ABCD.

The area of the trapezoid is equal to the product of the half-sum of the lengths of its bases and the height.

Savsd = (ВС + АD) * ВН / 2.

Then ВН = 2 * Savsd / (BC + AD) = 2 * 35 / (1 + 4) = 70/5 = 15 cm.

In triangle ABC, we will build the height of AK to the base of the BC.

AK = ВН = 15 cm, since AKВН is a rectangle.

Determine the area of the triangle ABC.

Savs = BC * AK / 2 = 1 * 15/2 = 7.5 cm2.

Answer: The area of triangle ABC is 7.5 cm2.

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