# What is the area of a circle with a diameter of 4, 9, and 11 ft?

Mar 29, 2018

The areas in $f {t}^{2}$ are:

$d = 4 \implies A = 4 \pi$

$d = 9 \implies A = \frac{81}{4} \pi$

$d = 11 \implies A = \frac{121}{4} \pi$

#### Explanation:

The area of a circle of radius $r$ is given by the well known formula:

$A = \pi {r}^{2}$

If the diameter is $d$ the we have $d = 2 r \implies r = \frac{d}{2}$, thus we have:

$A = \pi {\left(\frac{d}{2}\right)}^{2} = \frac{\pi {d}^{2}}{4}$

Thus, we have:

$d = 4 \implies A = \frac{\pi {4}^{2}}{4} = 4 \pi$

$d = 9 \implies A = \frac{\pi {9}^{2}}{4} = \frac{81}{4} \pi$

$d = 11 \implies A = \frac{\pi {11}^{2}}{4} = \frac{121}{4} \pi$