Find the area of an isosceles trapezoid with bases 2cm and 6cm if the angle for the larger base is a.

univerkov | September 3, 2021 | education

Let’s build the height of the CH.

Since the trapezoid ABCD is isosceles, the height CH divides the larger base into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases.

DН = (АD – ВС) / 2 = (6 – 2) / 2 = 2 cm.

In a right-angled triangle СDН the angle СDН = α0, then tgα = CH / DH.

CH = DH * tgα = 2 * tgα cm.

Determine the area of the trapezoid ABCD.

Savsd = (ВС + АD) * СН / 2 = (2 + 6) * 2 * tanα / 2 = 8 * tanα cm2.

Answer: The area of the trapezoid is 8 * tgα cm2.

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