Question

The figure below shows part of a stained glass window depicting the rising sun which function can be used to find the area of the region outside of the semicircle but inside the rectangle. (Look at the picture for more details)

Answer 1

We know that the area of a semicircle = 1/2(πr^2)

r = the radius

We also know that the area of a rectangle = xy

x = width

y = length

In our problem,

r = w

x = w

y = w + 5

A(w) = w(w + 5) - 1/2(πw^2)

Let's simplify the right side of the function.

A(w) = w^2 + 5w - 1/2πw^2