Question

A rectangular window is topped with a semicircle on top. the height of the rectangular part is 1 more than 3 times its width , w meters which function represents the total area?
A.) A(w) = w(1 + 3w) + pi(w/2)^2

B.) A(w) = w(1 + 3w) + pi(w/2)^2/2

C.) A(w) = w(1 + 3w) + pi(w)^2/2

D.) A(w) = w(1 + 3w) + pi(w)^2

Answer 1

In general for a rectangle of dimensions w by h and a semicircle of diameter w we get an area:

$A = wh + \frac 1 2 \pi (\frac w 2)^2$

The halfs are because a semicircle is half a circle and a radius is half a diameter.

We're told

$h = 1+ 3w$

Substituting,

$A(w) = w(1+3w) + \frac 1 2 \pi (\frac w 2)^2$

Answer: B