In trapezoid ABCD, the smaller diagonal BD is perpendicular to the base of AD and BC, the sum of the acute angles is 90 degrees. Find the area of the trapezoid if the base is AD = 2, BC = 18.
Let the angle BAD = X0.
Since, by condition, the angle (BAD + BCD) = 90, then the angle BCD = (90 – X) 0.
In a right-angled triangle ABD, the angle ABD = (90 – BAD) = (90 – X) 0, then the angle ABD = BCD, and therefore the triangles ABD and BCD are similar in acute angle.
In similar triangles ABD and BCD, AD / BD = BD / BC.
ВD ^ 2 = АD * ВС = 2 * 18 = 36.
ВD = 6 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * ВD / 2 = (2 + 18) * 6/2 = 60 cm2.
Answer: The area of the trapezoid is 60 cm2.
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