An isosceles trapezoid angle at the base = 60 °. One of the bases is 2 times larger

| March 17, 2021 | education

An isosceles trapezoid angle at the base = 60 °. One of the bases is 2 times larger than the other, and the side = 19 cm. Find the area of the trapezoid.

We draw from the vertices of the obtuse angles the heights of the ВН and СK.

In a right-angled triangle ABН, the angle ABН = 180 – 90 – 60 = 30, then the leg AH lies opposite the angle 30, which means its length is equal to half the length of the hypotenuse AB. AH = AB / 2 = 19/2 = 9.5 cm.

Since the trapezoid is isosceles, then DK = AH = 9, 5 cm.

Since, by condition, AD = 2 * BC, and НK = BC, since ВСKН is a rectangle, AH + DK = НK = BC = 9.5 + 9.5 = 19 cm.

From the right-angled triangle ABН, we determine the length of the ВН leg.

Sin60 = HВ / AB.

ВН = AB * Sin60 = 19 * √3 / 2 cm.

Determine the area of ​​the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (9.5 + 19) * (19 * √3 / 2) / 2 = 541.5 * √3 / 4 cm2.

Answer: The area of ​​the trapezoid is 541.5 * √3 / 4 cm2.



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