#### Answer

24 $in^{2}$

#### Work Step by Step

A circle is inscribed in a triangle having sides of length 6in, 8in, and 10in
the length of the radius of the inscribed circle is 2 in.
We need to find the area of the triangle
Where P represents the perimeter of a triangle and r represents the length of the radius of its inscribed circle, the area of the triangle is given by
A = $\frac{1}{2}$rP
Perimeter of triangle = 6+8+10 = 24 in
A = $\frac{1}{2}$rP
A = $\frac{1}{2}$*2*24 = 24 $in^{2}$