In a rectangular trapezoid ABCD, the large side is 8cm, the angle A = 60

| September 17, 2021 | education

In a rectangular trapezoid ABCD, the large side is 8cm, the angle A = 60 °, and the height BH divides the base of AD in half. Find the area of the trapezoid.

In a right-angled triangle ABН, we determine the value of the angle ABН. Angle ABH = 180 – AHB – BAН = 180 – 90 – 60 = 30. Then the leg AH lies opposite angle 30 and is equal to half the length of the hypotenuse AB. AH = 8/2 = 4 cm.

Then BH ^ 2 = AB ^ 2 – AH ^ 2 = 64 – 16 = 48.

BH = 4 * √3 cm.

By condition, BH divides AD in half, then AH = DH = 4 cm.

AD = AH + DH = 4 + 4 = 8 cm.

ВСDН is a rectangle, since ВН is height, and СDА = 90 by condition, then CB = DH = 4 cm.

Determine the area of the trapezoid.

Savsd = (СВ + AD) * ВН / 2 = (4 + 8) * 4 * √3 / 2 = 24 * √3 cm2.

Answer: The area of the trapezoid is 24 * √3 cm2.



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