In trapezoid ABCD, side AD = 20 cm and side AB = 15. Determine the area of the trapezoid if the angle
| May 20, 2021 | education
In trapezoid ABCD, side AD = 20 cm and side AB = 15. Determine the area of the trapezoid if the angle BCD = 45 and the angle BAD = 90
From the top D of the trapezoid, draw the height DH to the base of the BC.
Consider a triangle DHS, in which the angle НСD is equal to the angle ВСD and is equal to 45, the angle DHS is equal to 90, since DH is perpendicular to BC, then the angle НDC = 180 – 90 – 45 = 45, and the SDS triangle is isosceles and DH = СН = AB = 15 cm.
Segment BH = AD = 20 cm, then the base of the trapezoid BC = BH + HC = 20 + 15 = 35 cm.
Determine the area of the trapezoid.
S = DH * (AD + BC) / 2 = 15 * (35 + 20) / 2 = 412.5 cm2.
Answer: The area of the trapezoid is S = 412.5 cm2.
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