The two smaller sides of a rectangular trapezoid are 4 cm each, and one of the corners is 45 degrees. Find the area of the trapezoid.
| January 22, 2021 | education
From the top of the obtuse angle C, draw the height CH.
In the right-angled triangle СDН, according to the condition, the angle СDН = 450, then the angle СDН = 180 – 90 – 45 = 450, and the triangle СDН is equilateral, СD = DН = 4 cm.
Quadrangle ABCН is a rectangle, since BC is parallel to AD, and AB and CH are perpendicular to the bases of the trapezoid, then AH = BC = 4 cm, and the base of AD = AH + DН = 4 + 4 = 8 cm.
Determine the area of the trapezoid.
Savsd = (BC + AD) * CH / 2 = (4 + 8) * 4/2 = 24 cm2.
Answer: The area of the trapezoid is 24 cm2.
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