In an isosceles trapezoid with an acute angle of 30 degrees, the sum of the bases is 22 cm, and the perimeter

In an isosceles trapezoid with an acute angle of 30 degrees, the sum of the bases is 22 cm, and the perimeter is 30 cm. Find the area of the trapezoid.

The perimeter of the trapezoid is equal to the sum of the sides and bases:

p = AB + ED + (BE + AD);

30 cm = AB + ED + 22 cm;

AB + ED = 8 cm;

AB = ED (isosceles trapezoid);

AB + AB = 8 cm;

AB = 4 cm.

From the extreme point of the upper base, let us lower the height BF to the base AD

In the formed right-angled triangle ABF, leg BF is equal to half of side AB (leg opposite <A = 30 °):

BF = AB / 2 = 4 cm / 2 = 2 cm.

The area of the trapezoid is equal to the product of the half-sum of the bases and the height:

S = ((BE + AD) / 2) * BF = (22 cm / 2) * 2 cm = 22 cm ^ 2.

Answer: 2 cm ^ 2.