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

univerkov | 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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