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)

= `(("n"("n" + 1)(2"n" + 1))/6)_(n = 24) - (("n"("n" + 1)(2"n" + 1))/6)_("n" = 9)`

= `(24 xx 25 xx 49)/6 - (9 xx 10 xx 19)/6`

= 4900 – 285

= 4615

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