Final answer:
To find the area of a circle inscribed in a triangle bounded by certain lines, you need to find the intersection points of those lines, calculate the base and height of the triangle, and then use the formula A = 1/2 * base * height to find the area.
Step-by-step explanation:
To find the area of a circle inscribed in a triangle, we need to first find the length of the triangle's base and height. In this case, the triangle is bounded by the lines 3x - 4y + 1 = 0, 4x - y + 2 = 0, and x + 3y + 3 = 0.
We can find the intersection points of these lines and use them to calculate the base and height. Once we have the base and height, we can use the formula A = 1/2 * base * height to find the area of the triangle.