Question

Find the total area of $14$ square whose sides are $11cm,12cm,.....24cm$, respectively.

Answer 1

$S={11}^2+{12}^2+{13}^2+...+{24}^2$

We have $S=1^2+2^2+3^2+...+n^2=\frac{n(n+1)(2n+1)}{6}$

$\therefore S=(1^2+2^2+3^2+...+{24}^2)-(1^2+2^2+3^2+...+{10}^2)$

$=\frac{24\times 25\times (2\times 24+1)}{6}-\frac{10\times 11\times (2\times 10+1)}{6}$

$=\frac{24\times 25\times 49}{6}-\frac{10\times 11\times 21}{6}$

$=4900-385=4,515‬{cm}^2$