Question

How do you work this out

Answer 1

Check the picture below.

notice, is just a circle inscribed in a square.

now for the first one, we know the diameter is 14, so the square is a 14x14, and the radius of that is half the diameter or 7.

now, if we get the area of the square, which includes the area of the circle, and THEN get the area of the circle and subtract it from the square's, what's leftover is the shaded section.

$\bf \textit{area of a circle}\\\\ A=\pi r^2\\\\ -------------------------------\\\\ \stackrel{\textit{square's area}}{14\cdot 14}~-~\stackrel{\textit{circle's area}}{\pi 7^2}\implies 196-49\pi$

now, for the one on the right-hand-side, the radius is 8, and square's area is 16x16,

$\bf \stackrel{\textit{square's area}}{16\cdot 16}~-~\stackrel{\textit{circle's area}}{\pi 8^2}\implies 256-64\pi$