The perimeter of a triangle is 4, and the radius of the inscribed circle is 1/3. Find its area.

It is known from the condition that the perimeter of the triangle is 4, and the radius of the inscribed circle is 1/3. We need to find its area.

To solve the problem, we will apply the following properties.

It is known that the radius of a circle inscribed in an arbitrary triangle is equal to the ratio of its area to the floor perimeter.

Using a formula, we can write it like this:

r = S / p,

where p is the floor perimeter.

We know the perimeter from the condition, and we find the half perimeter as follows:

p = P / 2 = 4/2 = 2.

Find the area:

S = r * p = 1/3 * 2 = 2/3 sq. units.