Find the area of an isosceles trapezoid ABCD with a large base AD = 12cm, BC = 8cm, m (angle A) = 60 degrees.

univerkov | September 6, 2021 | education

From the top B of the trapezoid, draw the height BH.

Since the trapezoid is isosceles, the height BH divides the base of AD into segments AH and DH, the length of the smaller of which is equal to the half-difference of the lengths of its bases.

AH = (AD – BC) / 2 = (12 – 8) / 2 = 2 cm.

In a right-angled triangle ABN tg60 = BH / AH.

BH = AH * tg60 = 2 * √3 cm.

Determine the area of the trapezoid.

Str = (АD + ВС) * ВН / 2 = (12 + 8) * 2 * √3 / 2 = 20 * √3 cm2.

Answer: The area of the trapezoid is 20 * √3 cm2.

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