Find the approximate area of the shaded region below, consisting of a right triangle with a circle cut out of it. Use 3.14 as an approximation for PI
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An image shows a right triangle with a circle cut out of it. The legs that make up the right triangle are both 60 meters. The diameter of the circle cut out is 20 meters. All of the triangle is shaded, except where the circle is cut out.
A)544 square meters
B)3,286 square meters
C)314 square meters
D)1,486 square meters
To find the area of the shaded region, we first need to find the area of the right triangle and then subtract the area of the circle.
The area of a right triangle is given by the formula: A = (base * height) / 2. In this case, the base and height of the triangle are both 60 meters. Therefore, the area of the right triangle is (60 * 60) / 2 = 1,800 square meters.
The area of a circle is given by the formula: A = π * r^2. The diameter of the circle is 20 meters, so the radius (r) is half of that, which is 10 meters. Therefore, the area of the circle is 3.14 * (10^2) = 314 square meters.
To find the area of the shaded region, we subtract the area of the circle from the area of the right triangle: 1,800 - 314 = 1,486 square meters.
Therefore, the approximate area of the shaded region is 1,486 square meters.
The answer is D) 1,486 square meters.