# In an isosceles trapezoid ABCD, the diagonal AC is perpendicular to the side, angle D = 60 *,

In an isosceles trapezoid ABCD, the diagonal AC is perpendicular to the side, angle D = 60 *, AD = 20 cm, BC = 10 cm. Find the perimeter of the trapezoid.

Determine the value of the unknown angle of the triangle ABC. Angle CAD = 180 – 90 – 60 = 30.

The leg CD of the triangle is located opposite the angle 30, and, accordingly, its length is equal to half the length of the hypotenuse AD. СD = АD / 2 = 20/2 = 10 cm.

Since, by condition, the trapezoid ABCD is isosceles, then its lateral sides are equal – AB = CD = 10 cm.

Let’s define the perimeter of the trapezoid.

P = AB + BC + CD + AD = 10 + 10 + 10 + 20 = 50 cm.

Answer: The perimeter of the trapezoid is 50 cm.

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