ABCD is a rectangular trapezoid. Angle D = Angle C = 90 degrees BC = 3 CD = 6 BD

| May 19, 2021 | education

ABCD is a rectangular trapezoid. Angle D = Angle C = 90 degrees BC = 3 CD = 6 BD perpendicular to AB Find the area of the trapezoid.

Since the diagonal BD, by condition, is perpendicular to the lateral side AB, then the triangle ABD is rectangular, in which we draw the height BH to the hypotenuse AD.

Then, according to the property of the height of a right-angled triangle, drawn from the vertex of the right angle, the square of the length of the height is equal to the product of the segments into which the hypotenuse is divided.

BH ^ 2 = AH * DH.

AH = BH ^ 2 / DH.

Quadrangle BCDH is a rectangle, then BH = CD = 6 cm, DH = BC = 3 cm.

AH = 36/3 = 12 cm.

Then the length АD = АН + DH = 12 + 3 = 15 cm.

Determine the area of ​​the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (3 + 15) * 6/2 = 54 cm2.

Answer: The area of ​​the trapezoid is 54 cm2.



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