In an isosceles trapezoid ABCD with bases AD and BC and an area of 96 cm2
| June 25, 2021 | education
In an isosceles trapezoid ABCD with bases AD and BC and an area of 96 cm2, the CM height is drawn. Find the height of the trapezoid if AM = 12 cm.
In an isosceles trapezoid, the height, drawn and the tops of an obtuse angle, divides the larger base into two segments, the smaller one of which is equal to the half-difference of the bases, and the larger segment – the half-sum of the bases.
AM = (BC + AD) / 2 = 12 cm.
According to the formula for the area of the trapezoid: Savsd = (BC + AD) * CM / 2.
96 = 12 * CM / 2.
CM = 2 * 96/12 = 16 cm.
Answer: The height of the trapezoid is 16 cm.
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