Find the area of an isosceles trapezoid with bases 12cm and 22cm and a side 13cm.

univerkov | January 17, 2021 | education

From the top B of the trapezium, we draw the height BH, which in the isosceles trapezoid cuts off the segment AH equal to the half-difference of the bases.

AH = (22 – 12) / 2 = 10/2 = 5 cm.

Then, in a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the leg BН, which is the height of the trapezoid.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144.

BH = 12 cm.

Determine the area of the trapezoid.

Savsd = (BP + ВС) * ВН / 2 = (22 + 12) * 12/2 = 204 cm2.

Answer: The area of the trapezoid is 204 cm2.

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