10. PYQ - Find the area to be decorated

Rekha has \(21\) square colour papers of sizes \(3\) \(cm\), \(4\) \(cm\), \(5\) \(cm\), … \(24\) \(cm\). How much area can be decorated with these colour papers?

 

 

We know that, the sum of the squares of first \(n\) natural numbers \(=\) $\frac{i\left(i+i\right)\left(ii+i\right)}{i}$.

 

$3^2+4^2+5^2+...+{24}^2$ \(=\) \((1^2 + 2^2 + 3^2 + ... 24^2)\) ×-+ $1^2+2^2$

 

\(=\) \(-\)

 

Area can be decoreated \(=\) \(cm^2\)