In an isosceles trapezoid, side = 6cm smaller base = 10cm and smaller angle = 60 degrees Find the area and perimeter.

| August 2, 2021 | education

Let’s draw the height BH of the trapezoid ABCD.

In a right-angled triangle ABH, the angle ABH = (90 – BAD) = (90 – 60) = 30, then the leg AH is located opposite the angle 30, and then AH = AB / 2 = 6/2 = 3 cm.

By the property of an isosceles trapezoid, the height, which is drawn from an obtuse angle to the base, divides it into segments, the smaller of which is equal to the half-difference of the lengths of the bases of the trapezoid.

AH = (AD – BC) / 2.

Then AD = 2 * AH + BC = 2 * 3 + 10 = 16 cm.

Determine the height BH of the trapezoid. BH ^ 2 = AB ^ 2 – AH ^ 2 = 36 – 9 = 27.

BH = 3 * √3 cm.

Determine the perimeter of the trapezoid. P = 2 * AB + BC + AD = 2 * 6 + 10 + 16 = 38 cm.

Determine the area of ​​the trapezoid. Savsd = (ВС + АD) * ВН / 2 = (10 + 16) * 3 * √3 / 2 = 39 * √3 cm2.

Answer: The perimeter of the trapezoid is 38 cm, the area is 39 * √3 cm2.



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