Help me with a math problem (Functions)?

Question

So this window is x by 2x with a semicircle at the top. What is the function that represents the semicircle? I can't get beyond *pie*x^2/2. I know it's wrong I just don't know how to make it right. Any takers?

The area of the semi-circle...

Answer 1

Windows of this sort are almost always made with the semicircle mounted atop the short side, so that the window assumes a portrait or vertical orientation.

The area formula for a circle is:

A = π r².

Since we assume, and we have more than a 50% chance of being correct, that the semicircle is mounted atop the short side, then the radius of the semicircle is r = x/2. Its area is ½ the area of a circle with that radius. Thus, its area is:

A = ½ [π (x/2)²] = ½ [(π x²) / 4] = (1/8) π x².

If the semicircle is mounted atop the long side of the window, then its radius is 2x/2 = x and its area is:

A = ½ [π (2x/2)²] = (½) π x², which is 4 times the area of the semicircle in the other scenario.

Answer 2

The area is 0.5 π r² , where r is the radius. I can't tell from your description how the window is shaped long side up or short side up so

r = 1/2 x or r = x

So it's either 0.5 π (1/4) x²

or 0.5 π x²
.
.