In the trapezoid ABCD AD = 4, BC = 1, and its area is 35. Find the area of the triangle ABC.

univerkov | August 13, 2021 | education

Let us construct the height BH of the trapezoid and determine its length through the formula for the area of the trapezoid.

Savsd = (BC + AD) * BH / 2.

BH = 2 * Savs / (BC + AD) = 2 * 35/5 = 14 cm.

Let’s build the height AK of the triangle ABC. Since BH and AK are perpendicular to the bases AD and BC, then AKBN is a rectangle, and AK = BH = 14 cm.

Then Savs = BC * AK / 2 = 1 * 14/2 = 7 cm2.

Answer: The area of triangle ABC is 7 cm2.

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