Final answer:
The area of the equilateral triangle inscribed in a circle of radius 10 cm is 100√3 cm². The area shaded can be found by subtracting the area of the triangle from the area of the circle, resulting in 100π - 100√3 cm².
Step-by-step explanation:
To find the area of an equilateral triangle inscribed in a circle, we can use the formula A = (√3/4) * s^2, where A is the area and s is the length of each side of the triangle. Since the triangle is equilateral, the length of each side is equal to the diameter of the circle. In this case, the diameter is 2 * the radius, which is 2 * 10 cm. Therefore, the length of each side of the triangle is 20 cm. Substituting this value into the formula, we get A = (√3/4) * 20^2 = 100√3 cm².
To find the area shaded, we need to subtract the area of the equilateral triangle from the area of the circle. The area of the circle is given by the formula A = π * r^2, where A is the area and r is the radius. In this case, the radius is 10 cm. Substituting this value into the formula, we get A = π * 10^2 = 100π cm². Subtracting the area of the triangle (100√3 cm²) from the area of the circle (100π cm²), we find that the area shaded is 100π - 100√3 cm².