Final answer:
To determine the area of a circle inscribed in a triangle, we need to find the radius of the circle using properties of the triangle. The radius can be calculated using the area of the triangle and its semi-perimeter. The area of the circle is then found using the formula πr².
Step-by-step explanation:
To find the area of a circle inscribed in a triangle bounded by the given lines, it helps to determine the type of triangle and the position of the inscribed circle. For the purpose of this explanation, let's assume we've identified the triangle and its vertices, and we know that an inscribed circle (or incircle) touches each side of the triangle at a single point. The area of the incircle can be found using the formula for the area of a circle, which is πr², where r is the radius of the circle.
Given the information about the sides of the right triangles being 5 cm, 12 cm, and 13 cm, we can infer that these sides are part of the larger triangle's geometry. Since those measurements follow the Pythagorean theorem, we have a right-angled triangle, allowing us to apply specific properties of right-angled triangles to find the radius of the inscribed circle.
Generally, the radius of the incircle of a right-angled triangle can be calculated by taking the area of the triangle and dividing it by the semi-perimeter. However, calculating this for the given lines would require us to first find the coordinates of the vertices of the triangle by solving the equations of the lines, then use Heron's formula to find the area of the triangle, and finally calculate the semi-perimeter.