Question

23. Write and factor an expression that

makes the computation for finding the
area of the shaded region.

Answer 1

so hmmm the larger containing circle has a radius of "x", whilst there are four small circles in it with a radius of "y".

Now, if we get the area of the containing circle and get the area of the smaller circles and subtract the area of the smaller circles from that of the containing larger circle, what's leftover is what we didn't subtract, the shaded region.

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{containing circle} }{\pi x^2}~~ - ~~\stackrel{ \textit{four small circles} }{4(\pi y^2)}}\implies \stackrel{ \textit{shaded region} }{{\Large \begin{array}{llll} \pi x^2-4\pi y^2 \end{array}}}`