Question

A square has sides of length 12 inches. Find the exact AREA of its inscribed circle

Answer 1

Since the circle is inscribe in the square, the lenght of the square will in turn be the diameter of the circle.

`\begin{gathered} \text{length of square =diameter of circle} \\ l=d \\ 12in=d \\ \text{Therefore diameter of the circle is 12 inches.} \\ \end{gathered}`

The area of a circle is calculated with the formula:

`\pi r^2`
`\begin{gathered} r=(d)/(2) \\ r=(12)/(2) \\ r=6in \end{gathered}`

Substitute this value into the formula for area of a circle:

`\begin{gathered} \pi r^2 \\ 3.14*6^2 \\ 3.14*36 \\ 113.04in^2 \end{gathered}`

The area of the inscribed circle is 113.04 square inches.