Question

5. Find the total area of 12 squares whose sides are 12 cm, 13cm, g, 23cm. respectively.

Answer 1

Find the total area of 12 squares whose sides are 12 cm,13 cm,....... 23 cm respectively.

Area of square = (side length)²
There are 12 squares whose sides are 12, 13, 14, ........ 23
so, area of square are 12² , 13² , 14² , .......23²
we know, sum of square of natural number = n(n +1)(2n+1)/6
12² + 13² + ......23² = (1² + 2² + 3² + ..... + 23²) - (1² + 2² + ..... 11²)
= S₂₃ - S₁₁
= 23(23 + 1)(23 × 2 + 1)/6 - 11(11 + 1)(11 × 2 + 1)/6
= (23 x 24 x 47)/6 - (11 x 12 x 23)/6
= 4324 - 506
= 3818

Answer 2

HELLO DEAR,


WE KNOW THAT:-
area of Square = (side)²
so, Total surface area of 12 squares = 12² + 13² + ......... + 23²

and

Sum of squares of n natural numbers = n(n+1)(2n+1)/6

(12² + 13² + 14² + .......+ 23²)

                 = (1² + 2² + ......... + 23²) - (1² + 2² + ......... + 11²)

                   = [23(23+1)(2*23+1)]/6 - [11(11+1)(2*11+1)]/6

                   = (23 * 24 *  47)/6 - (11 * 12 * 23)/6

                   = 4324 - 506

                  =  3818




I HOPE ITS HELP YOU DEAR,
THANKS