Calculate the area of the trapezoid in which the bases are 5 cm and 12 cm, and the acute angle is 30 degrees.

univerkov | April 20, 2021 | education

Let’s finish the height of the HВ trapezoid.

The height of the trapezoid, drawn from the top of the obtuse angle to the larger base, divides the base into two segments, the length of the smaller of which is equal to the half-difference of the bases.

AH = (AD – BC) / 2 = (12 – 5) / 2 = 7/2 cm.

In a right-angled triangle AВН, tg30 = ВН / AН.

BH = AH * tg30 = (7/2) * (1 / √3) = 7 * √3 / 6.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (5 + 12) * (7 * √3 / 6) / 2 = (119/6) * √3 cm2.

Answer: The area of the trapezoid is (119/6) * √3 cm2.

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