A rectangular trapezoid with a perimeter of 36 cm and a larger side equal to 10 cm

A rectangular trapezoid with a perimeter of 36 cm and a larger side equal to 10 cm is described around the circle. Find the area of the circle.

One of the properties of a trapezoid says that a circle can be inscribed into a trapezoid only if the sums of the bases and sides are equal.
In this problem, the two sides have:
36/2 = 18 (cm).
Large side 10 cm (provided), which means the smaller side:
18 – 10 = 8 (cm).
The smaller flank is the height of the trapezoid and the diameter of the inscribed circle.
r = d / 2 = 4 (cm).
Find the area of the circle:
S = π * r² = 3.14 * 16 = 50.24 (cm²).
Answer: the area of the circle is 50.24 cm².