Find the area of a circle inscribed in a triangle with sides 4 cm, 13 cm, 15 cm.

Let us find out what the half-perimeter of our triangle will equal if from the condition it is known that the lengths of its sides correspond to 4, 13 and 15 centimeters:
(13 + 15 + 4): 2 = 16.
Let’s find out how many square centimeters the area of such a geometric figure is expressed:
√ (16 (16 – 15) (16 – 13) (16 – 4)) = √ (16 * 1 * 3 * 12) = √576 = 24.
Let us determine what the radius will be under the following conditions:
24/16 = 6/4 = 1.5.
Let’s determine what the area of a circle with such a radius will be:
1.5 * 1.5 * 3.14 = 7.065.
Answer: 7.065 cm2.