# The bases of the trapezoid are equal to 4 and 25, one of the lateral sides is equal, and the angle between

January 30, 2021 | education

| **The bases of the trapezoid are equal to 4 and 25, one of the lateral sides is equal, and the angle between it and one of the bases is equal. Find the area of the trapezoid.**

Let’s build the height of the HВ trapezoid of AВСD. In a right-angled triangle ABН, the angle ABН = ABC – СВН = 135 – 90 = 450.

Then the triangle ABН is rectangular and isosceles, AH = BH.

AB ^ 2 = 2 * BH ^ 2.

BH ^ 2 = AB ^ 2/2 = 49 * 2/2 = 49.

BH = 7 cm.

Then Savsd = (ВС + AD) * ВН / 2 = (4 + 25) * 7/2 = 101.5 cm2.

Answer: The area of the trapezoid is 101.5 cm2.

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