The bases of the trapezoid are 11 and 27 and its perimeter is 72. Find the area of the trapezoid.

Let us determine the sum of the lengths of the sides of the trapezoid.

AB + CD = Ravs – (BC + AD) = 72 – (11 + 27) = 34 cm.

Then AB = CD = 34/2 = 17 cm.

We construct the height BH, which divided the larger base AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the trapezoid bases.

AH = (AD – BC) / 2 = (27 – 11) / 2 = 8 cm.

In the right-angled triangle ABN, according to the Pythagorean theorem, we determine the length of the leg AN.

AH ^ 2 = AB ^ 2 – BH ^ 2 = 289 – 64 = 225.

AH = 15 cm.

Determine the area of the trapezoid.

Savsd = (ВС + АD) * ВН / 2 = (11 + 27) * 15/2 = 285 cm2.

Answer: The area of the trapezoid is 285 cm2.