In an isosceles trapezoid with an acute angle of 30 °, the side is exactly 6 cm and the perimeter

In an isosceles trapezoid with an acute angle of 30 °, the side is exactly 6 cm and the perimeter is 56 cm. Find the area of the trapezoid.

Let’s build the height of the ВН, which in the right-angled triangle AВН is located opposite the angle 30, then ВН = AB / 2 = 6/2 = 3 cm.

The sum of the sides of the trapezoid is: (AB + CD) = 6 + 6 = 12 cm.

Then the sum of the lengths of the bases of the trapezoid will be: (BC + AD) = Ravsd – 12 = 56 – 12 = 44 cm.

Then the area of the trapezoid is:

Savsd = (ВС + АD) * ВН / 2 = 44 * 3/2 = 66 cm2.

Answer: The area of the trapezoid is 66 cm2.