Question

What is the area of the shaded (yellow) region?

Answer 1

well, looking at the picture above, we can see that the diameters are 12.5 and 3.5 for those circles, that means the radii for them will be half that for each, namely 6.25 and 1.75 respectively.

let's get the whole area for containing circle, and then subtract the area of the small ones, what's leftover is the shaded area.

`\stackrel{large~one}{\textit{area of a circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=6.25 \end{cases}\implies A=\pi 6.25^2 \\\\\\ \stackrel{small~one}{\textit{area of a circle}}\\\\ A=\pi r^2 ~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ r=1.75 \end{cases}\implies A=\pi 1.75^2 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{\LARGE Areas}}{\stackrel{large}{\pi 6.25^2}~~ - ~~\stackrel{\textit{two small ones}}{2(\pi 1.75^2)}} ~~ \approx ~~ \text{\LARGE 103.48}`

Answer 2

103.42

Explanation:

use the big circle area - 2 little white circles' area

big r = 12.5/2 = 6.25 so big circe area = π r² =π * 6.25²

small r = 3.5/2 = 1.75 so small circe area = π r² =π * 1.75²

2 of them = 2π * 1.75²

so π 6.25² - 2π * 1.75² = 39.06π-6.13π=103.42