Calculate the area of the trapezoid ABCD with the base AD and BC if AD = 24 cm, BC = 16 cm
| February 25, 2021 | education
Calculate the area of the trapezoid ABCD with the base AD and BC if AD = 24 cm, BC = 16 cm, angle A = 45 degrees, angle D = 90 degrees.
Let’s finish the height of the ВН.
Quadrangle ВСDН is a rectangle, since ВН is a height, and a trapezoid is rectangular, then DH = ВС = 16 cm.
The length of the segment is АН = АD – DH = 24 – 16 = 8 cm.
In the formed right-angled triangle ABН, one of the acute angles is 45, then the right-angled triangle ABН is isosceles, AH = BH = 8 cm.
Determine the area of the trapezoid.
Savsd = (ВС + АD) * ВН / 2 = (16 + 24) * 8/2 = 160 cm2.
Answer: The area of the trapezoid is 160 cm2.
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