The height of an isosceles trapezoid drawn from the top of an obtuse angle and dividing the larger base into

univerkov | August 3, 2021 | education

The height of an isosceles trapezoid drawn from the top of an obtuse angle and dividing the larger base into two segments, one of which is equal to half of the smaller base, is 6cm. The larger base is 2cm larger than the smaller one. Find the area of the trapezoid.

According to the condition, AD – BC = 2 cm.Then AP + CH = 2 cm.

Since the trapezoid is isosceles, then AP = DH, then 2 * DH = 2 cm. DH = AP = 2/2 = 1 cm.

Also, by condition, BC = 2 * DH = 2 * 1 = 2 cm.

Quadrilateral BPНС is a rectangle, then PH = BC = 2 cm.

Base length AD = AP + DH + BH = 1 + 1 + 2 = 4 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * СН / 2 = (2 + 4) * 6/2 = 18 cm2.

Answer: The area of the trapezoid is 18 cm2.

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