9751 /www/nrich/html/content/id/9751/ 1 2013-01-02T17:09:49 <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image src="squares%20in%20circle.png" style="float: right;"></mdo:image><br></br> <br></br> <br></br> The diagram shows a pattern of eight equal shaded squares inside a circle of area $\pi$ square units.<br></br> <br></br> <br></br> What is the area (in square units) of the shaded region?<br></br></mdoxml> <?xml version="1.0" encoding="UTF-8"?> <mdoxml version="1.0"><mdo:image src="squares%20in%20circle2.png" style="float: right;"></mdo:image> Let the centre of the circle be $O$ and let $A$ and $B$ be corners of one of the shaded squares, as shown.<br></br> <br></br> As the circle has area $\pi$ square units, its radius is $1$ unit. So $OB$ is $1$ unit long.<br></br> <br></br> Let the length of the side of each of the shaded squares be $x$ units.<br></br> By Pythagoras&#39;s Theorem, $OB^2 = OA^2 + AB^2$, that is $1^2 = (2x)^2 + x^2$.<br></br> So $5x^2=1$. Now the total shaded area is $8x^2 = 8 \times \frac{1}{5} = 1 \frac{3}{5}$ square units.</mdoxml> 2 3 0 0 1 0 0 Weekly Problem 5 - 2013 ajk44 Alison's dev tag