A trapezoid with a smaller diagonal is perpendicular to the bases the sum
| June 15, 2021 | education
A trapezoid with a smaller diagonal is perpendicular to the bases the sum of acute angles is 90 find the area of a trapezoid if its rigging is 2 and 18
Since the diagonal BD is perpendicular to the bases, the triangles ABD and BCD are rectangular.
By condition, the angle BAD + BCD = 90, then the angle BCD = 90 – BAD.
In triangle ABD, angle ABD = 90 – BAD. Then right-angled triangles ABD and BCD are similar in acute angle.
Their similarities are triangles: AD / BD = BD / BC.
ВD ^ 2 = АD * ВС = 18 * 2 = 36.
ВD = 6 cm.
The area of the trapezoid is equal to: Savsd = (АD + ВС) * ВD / 2 = (18 + 2) * 6/2 = 60 cm2.
Answer: The area of the trapezoid is 60 cm2.
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