The shaded region of the circle has a diameter of 43m and a height of 1.5m
14. Find the area of the shaded region. Round your answer to the nearest tenth.
4712.4 m^2
4057 m^2
195.6 m^2
1138 m^2
The area of the shaded region can be calculated by subtracting the area of the triangle from the area of the circle.
The area of the circle is A = πr^2, where r is the radius. Since the diameter is 43m, the radius is half of that: r = 43m / 2 = 21.5m.
So, the area of the circle is A = π(21.5)^2 ≈ 1451.1 m^2.
The area of the triangle is given by A = 0.5bh, where b is the base (which is the diameter of the circle) and h is the height of the triangle (1.5m).
So, the area of the triangle is A = 0.5 * 43m * 1.5m = 32.25 m^2.
Subtracting the area of the triangle from the area of the circle gives us the area of the shaded region: 1451.1 m^2 - 32.25 m^2 ≈ 1418.85 m^2.
Rounding to the nearest tenth, the area of the shaded region is 1418.9 m^2.
Therefore, the closest option is 1138 m^2.