Find the area of the trapezoid if its smaller base is BC = 12 cm, AB = CD, angle D = 45, the height of the trapezoid is 8 cm.

univerkov | May 18, 2021 | education

Let’s build the heights BH and CM of the trapezoid ABCD.

Quadrangle BCMН is a rectangle, then НM = BC = 12 cm.

The СDM triangle is rectangular with an acute angle of 45, then this triangle is also isosceles, DM = CM = 8 cm.

Rectangular triangles ABН and CDM are equal in hypotenuse and leg, then AH = DM = 8 cm.

Base length АD = АН + НМ + DМ = 8 + 12 + 8 = 28 cm.

Then Savsd = (BC + AD) * CM / 2 = (12 + 28) * 8/2 = 160 cm2.

Answer: The area of the trapezoid is 160 cm2.

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