find the area of a triangle that has an inscribed circle with a circumference of 8pi cm, and which has a perimeter of 18cm.

Answer: The area of the triangle is 36cm^2

Step-by-step explanation:

Extracting important information from the question:-

** * The triangle has a perimeter of 18cn.

** * The inscribed circle in the triangle has a circumference of 8pi cm (8π cm).

In order, to find the area of this triangle, the radius of the inscribed circle is required.

Since the circumference of the circle is 8π cm and the formula for finding the circumference of a circle is 2πr, we can then derive the circle's radius by substituting appropriately and making "r" the subject of the formula.

C = 2πr

2πr = 8π

r = 8π/2π

r = 4cm

The formula for finding the area of a triangle that has a circle inscribed in it is:

A = 1/2 * r * (the triangle's perimeter)

Recall that the perimeter of the triangle is 18cm and now the radius of the inscribed circle is discovered to be 4cm.

We then substitute and solve:

(1/2) * 4 * 18

= 2 * 18

= 36cm^2