Answer:25sqrt3-25pi/3
Step-by-step explanation:
Assuming the triangle is equilateral, we clearly need to find the radius of the circle, and subtract from the entire area of the triangle.
First, the area of an equilaterail triangle is given by the formula s^2 *sqrt3/4.
Next, the connect the center of the radius to points of tangency. Note this bisects the angle of the equilateral triangle into a 30 degree angle, and connecting radii to points of tangency forms a 90 degree angle, so this is a 30-60-90 triangle. This bisects the side length of the triangle, and the ratio of sides of a 30-60-90. Set this length as x. Thus, we have 4x^2=x^2+25, so 3x^2 =25. Dividing both sides by 3, we get x^2=25/3. Note that we only need x^2, as the formula is x^2 * pi. Hence, the area of the shaded region is 25sqrt3-25pi/3.
