In a rectangular trapezoid ABCD, a smaller base is 9 cm, a larger base is 12 cm.
| August 15, 2021 | education
In a rectangular trapezoid ABCD, a smaller base is 9 cm, a larger base is 12 cm. Angle D = 135 degrees, angle A = 90 degrees. Find the height of the trapezoid.
From the top of the obtuse angle of the trapezoid, we lower the height DH.
Quadrangle ABCН is a rectangle, then side BH = AD = 9 cm.
Segment СН = ВС – ВН = 12 – 9 = 3 cm.
In a right-angled triangle СDН, we define the values of acute angles. Angle СDН = СDА – НDА = 135 – 90 = 45, then angle НСD = 180 – 90 – 45 = 45, then triangle СDН is isosceles, СН = DH = 3 cm.
Determine the area of the trapezoid.
Savsd = (AD + BC) * CH / 2 = (9 + 12) * 3/2 = 31.5 cm2.
Answer: The area of the trapezoid is 31.5 cm2.
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