In an isosceles trapezoid, the bases are 5 cm and the angle at the base is 17 cm equal to 45 degrees. Find the area.
September 21, 2021 | education
| The area of the trapezoid is equal to the product of half the sum of the bases and the height. S = (BC + AD) / 2 * BM
We need to find the height of BM. Consider the triangle ABM. It is rectangular and isosceles, because angle M = 90 degrees, angle A = angle B = 45. So AM = BM.
Because the trapezoid is isosceles, then AM = ND, and BM = (AD – BC) / 2.
BM = (17 – 5) / 2 = 12/2 = 6 (cm)
S = (5 + 17) / 2 * 6 = 22/2 * 6 = 11 * 6 = 66 (cm ^ 2)
Answer. 66 cm ^ 2.
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