Find the area of a trapezoid in which the bases are 7 and 5, and one of the sides, equal to 6

univerkov | September 1, 2021 | education

Find the area of a trapezoid in which the bases are 7 and 5, and one of the sides, equal to 6, forms an angle of 30 ° with the base.

Let’s build the height BH of the trapezoid ABCD.

Triangle ABH is rectangular, in which the angle BH, by condition, is equal to 30, then the length of the leg BH, which lies opposite this angle, is equal to half the length of the hypotenuse AB.

BH = AB / 2 = 6/2 = 3 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (5 + 7) * 3/2 = 18 cm2.

Answer: The area of the trapezoid is 18 cm2.

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