Question

Please help me, make sure to tell me the answer, why it is the answer, and how it is the answer

Answer 1

Answer: it's the top right corner but i'm not sure.

Answer 2

Step One

Calculate the area of both the skating area and the spectator area.

Area = L * W

L = 4x

W = 4x

Area = 4x * 4x

Area = 16x^2

Step Two.

Find the radius of the semicircle. R = radius

From the diagram

R = The full length - the length given in the red shaded area.

R = 4x - 2x

R = 2x

Step Three

Find the area of the semicircle.

Area of a full circle = pi R^2

Area of a 1/2 circle =
`(\pi *(2x)^2)/(2)`

Area of a 1/2 circle =
`(\pi *4*x^2)/(2)`

Area of a 1/2 circle =
`\frac{\pi *2*x^2}{}`

Notice that the 2 in the denominator cancels in part with the 4 in the numerator.

Step Four

Find the area of the shaded area

Area of the shaded Area = Whole Area - Area of the Semi Circle.

Area of the shaded Area = 16x² -
`\frac{\pi *2*x^2}{}`

The answer is the upper right corner choice I think