The sides of the triangle are in the ratio 4:13:15, the radius of the circle inscribed in the triangle is 6.

The sides of the triangle are in the ratio 4:13:15, the radius of the circle inscribed in the triangle is 6. Determine the area of the triangle.

By connecting the vertices of the triangle with the center of the circle, we get three triangles. The height of each triangle is the radius of the inscribed circle. Area of a triangle:

S = 1/2 R * a + 1 / 2R * b + 1 / 2R * c;

2S = R * (a + b + c);

S = R * (a + b + c) / 2;

S = 6 * (4 + 13 + 15) / 2;

S = 3 * 32 = 96.

Answer: The area of a triangle is 96 square units.