In isosceles trapezoid ABCD, diagonal BD is perpendicular to the lateral side

| February 12, 2021 | education

In isosceles trapezoid ABCD, diagonal BD is perpendicular to the lateral side, angle A = 60 degrees, AD = 24cm, BC = 12cm. Find the perimeter of the trapezoid.

We will also draw the peaks in the height of the ВН.

The height drawn and the tops of the obtuse angle of the trapezoid divides the larger base into two segments, the smaller of which is equal to the half difference of the bases. AH = (AD – BC) / 2 = (24 – 12) / 2 = 12/2 = 6 cm.

Then in the right-angled triangle ABН the acute angle ABН = 180 – 90 – 60 = 300. The leg AН lies opposite the angle 300, and therefore its length is equal to half the length of the hypotenuse AB.

AB = AH * 2 = 6 * 2 = 12 cm.

Since the trapezoid is isosceles, then СD = AB = 12 cm.

Let’s define the perimeter of the trapezoid.

Ravsd = AB + BC + СD + AC = 12 + 12 + 12 + 24 cm = 60 cm.

Answer: The perimeter of the trapezoid is 60 cm.



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