In an isosceles trapezoid ABCD with bases BC and AD, the angle B is 120 degrees, BC = 8cm, AD = 10cm.
| January 29, 2021 | education
In an isosceles trapezoid ABCD with bases BC and AD, the angle B is 120 degrees, BC = 8cm, AD = 10cm. Find the area of the trapezoid.
Let’s draw the height of the CH trapezoid. Since the trapezoid is isosceles, the height of the CH divides the base of the BP into two segments, the smaller of which is: DН = (AD – BC) / 2 = (10 – 8) / 2 = 1 cm.
In a right-angled triangle CDH, the angle is DСН = (ВСD – ВСН) = (120 – 90) = 30.
The DН leg lies opposite the angle 30, then tg30 = DН / CH.
СН = DН / tg30 = 1 / (1 / √3) = √3 cm.
Determine the area of the trapezoid.
Savsd = (ВС + AD) * CH / 2 = (8 + 10) * √3 / 2 = 9 * √3 cm2.
Answer: The area of the trapezoid is 9 * √3 cm2.
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