The circle below has a diameter of 12 inches. Find the area of the shaded area in the figure below.
A circle has a triangle inside. The corners of the triangle touch the outside edge of the circle. The triangle has a height of 10 inches and a base of 7 inches.
The circle below has a diameter of 12 inches. Find the area of the shaded area in the figure below.
A circle has a triangle inside. The corners of the triangle touch the outside edge of the circle. The triangle has a height of 10 inches and a base of 7 inches.
148.04 in2
113.04 in2
78.04 in2
35 in2
To find the area of the shaded region, we first need to find the area of the circle and the area of the triangle.
The area of a circle is calculated using the formula A = πr^2, where r is the radius of the circle. In this case, the diameter is given as 12 inches, so the radius is half of that, or 6 inches.
Area of the circle = π(6 inches)^2 = 36π square inches (approximately 113.04 square inches)
The area of a triangle is calculated using the formula A = (1/2)bh, where b is the base of the triangle and h is the height. In this case, the base is given as 7 inches and the height is given as 10 inches.
Area of the triangle = (1/2)(7 inches)(10 inches) = 35 square inches
To find the shaded area, we subtract the area of the triangle from the area of the circle.
Shaded area = Area of the circle - Area of the triangle = 113.04 - 35 = 78.04 square inches
Therefore, the area of the shaded region is 78.04 in2.