Find the area in an isosceles trapezoid if the bases are 11 and 7 cm, and the acute angle is 60 degrees.

univerkov | February 20, 2021 | education

Let’s stand the height of the CH trapezoid.

According to the property of the height of an isosceles trapezoid drawn to the larger base, the length of the DН segment is equal to the half-difference of the lengths of the bases of the trapezoid.

DН = (AD – BC) / 2 = (11 – 7) / 2 = 4/2 = 2 cm.

Let’s calculate the height through the tangent of the angle in the СDН triangle. tgСDН = СН / DН.

СН = DН * tgСДН = 2 * tg60 = 2 * √3 cm.

Determine the area of the trapezoid.

Savsd = (BC + AD) * CH / 2 = (7 + 11) * √3 / 2 = 9 * √3 cm2.

Answer: The area of the trapezoid is 9 * √3 cm2.

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