An isosceles trapezoid is given. Lateral side 18 cm, acute angle 60 °. The smaller base

| May 16, 2021 | education

An isosceles trapezoid is given. Lateral side 18 cm, acute angle 60 °. The smaller base of the trapezoid is 10cm. Find height, area, and perimeter.

From the top of the obtuse angle B, we lower the height BH of the trapezoid In the formed right-angled triangle ABН, the angle BAН, by condition, is 60, then the angle ABН = 180 – 90 – 60 = 30.

Leg AH lies opposite angle 30, which means that its length is equal to half the length of the hypotenuse AB.

AH = AB / 2 = 18/2 = 9 cm.

Determine the value of the height BH.

BH = AB * Sin60 = 18 * √3 / 2 = 9 * √3 cm.

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

AH = (AD – BC) / 2.

9 = (AD – 10) / 2.

18 = AD – 10.

AD = 28 cm.

Let’s define the perimeter of the trapezoid. P = AB + BC + CD + D = 18 + 10 + 18 + 28 = 74 cm.

Determine the area of ​​the trapezoid.

S = (ВС + АD) * ВН / 2 = (10 + 28) * 18/2 = 342 cm2.

Answer: The height is 9 * √3 cm, the perimeter is 74 cm, the area is 342 cm2.



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