Question

Rekha has 15 square colour papers of sizes 10 cm,11 cm,12 cm, …, 24 cm. How much area can be decorated with these colour papers?

Answer 1

10² + 11² + 12² + … + 24² 

= (1² + 2² + … + 24²) – (1² + 2² + … + 9²)

= ${\displaystyle {\left(\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{6}\right)}_{n=24}-{\left(\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{6}\right)}_{\text{n}=9}}$

= ${\displaystyle \frac{24\times 25\times 49}{6}-\frac{9\times 10\times 19}{6}}$

= 4900 – 285

= 4615

∴ Rekha has 4615 cm² colour papers. She can decorate 4615 cm² area with these colour papers.