Question

The diagram shows a circle drawn inside a square.

12 cm
6 cm
The circle has a radius of 6 cm.
The square has a side of length 12 cm.
Work out the shaded area.
Give your answer in terms of TT.

Answer 1

area of a triangle- pi x radius squared,
6^2 x pi = 36pi or 113.0973355,
area of a square- length x length
12 x 12 = 144
144 - 36pi = 30.90266447
you then have to divide this by 4 as you have quarter of what has just been worked out.

30.90266447 / 4 = 7.725666118
then divide this by pi
which would give you (x)TT
there may be a simpler way however this is how i have worked it out

Answer 2

let's get the whole area of the square, then the whole area of the circle, and subtract the area of the circle from that of the square, in essence making a hole in the square, what's leftover is what we didn't subtract, namely 4 shaded areas as you see in the picture below, then since they're 4 equal shaded areas, let's only grab a quarter of that, and that's the one shaded area in one corner.

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{square}{(12)(12)}~~ - ~~\stackrel{ circle }{\pi (6)^2}}\implies 144-36\pi \hspace{5em}\stackrel{ \textit{one quarter of that} }{\cfrac{144-36\pi}{4}\implies} {\Large \begin{array}{llll} 36-9\pi \end{array}}`