Question

Help please. Also include how to find region of shape equation (if there is one) thanks.

Answer 1

Check the picture below.

we can think of this as having two circles, one with a radius of 10, and a smaller one with a diameter of 10, so it has a radius of half that or 5.

Now, let's take the whole area of the larger one, then use only one quarter of it, only one quadrant, then get the area of the smaller one, and take half of that, then subtract that half from the quarter of the larger one.

What's leftover is what we didn't subtract, namely the shaded region.

`\stackrel{ \textit{\LARGE Large} }{\textit{Area of a Circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=10 \end{cases}\implies A=\pi (10)^2\implies A=100\pi \\\\[-0.35em] ~\dotfill\\\\ \stackrel{ \textit{\LARGE Small} }{\textit{Area of a Circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=5 \end{cases}\implies A=\pi (5)^2\implies A=25\pi \\\\[-0.35em] ~\dotfill`

`\stackrel{ \textit{\LARGE Areas} }{\stackrel{ \textit{one quadrant} }{\cfrac{1}{4}\cdot 100\pi} ~~ - ~~\stackrel{ \textit{half } }{\cfrac{1}{2}\cdot 25\pi}} \implies 25\pi -12.5\pi \implies {\Large \begin{array}{llll} 12.5\pi~cm^2 \end{array}}`