In an isosceles trapezoid, one of the bases is 2 times larger than each of the other sides.

| April 10, 2021 | education

In an isosceles trapezoid, one of the bases is 2 times larger than each of the other sides. Find the area of a trapezoid if its height is h.

By condition, AB = BC = CD, and AD = 2 * BC.

Let the length of the sides AB = BC = CD = X cm, then AD = 2 * X cm.

Let’s draw the heights of the  and CK Quadrangle ВСKN is a rectangle, then KН = BC = X cm.

AH = DH since the trapezoid is isosceles, then (AH + DH) = 2 * X – X = X cm.

AH = DH = X / 2.

In a right-angled triangle ABН, the leg AH is equal to half the length of the hypotenuse AB, then the angle ABН = 30. Then Cos30 = BH / AB = h / X.

X = h / Cos30 = h / (√3 / 2) = 2 * h / √3 cm.

Then AD = 4 * h / √3 cm.

Determine the area of ​​the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (2 * h / √3 + 4 * h / √3) * h / 2 = 6 * h ^ 2 / √3 / 2 = 3 * h ^ 2 / √ 3 = h ^ 2 * √3 cm2.

Answer: The area of ​​the trapezoid is h2 * √3 cm2.



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