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

Dear Student,

Please find the below required solution.

Given that the side of 12 square are 12, 13, 14, 15, ... , 23 (in cm)

And area of square = (side)²  
So area of 12 square whose sides are 12, 13, ......, 23 (in cm) is 12², 13², 14², ......, 23² (in cm²)

Hence total area of 12 square = 12²+13²+14²+ ......, +23²
                                                
                                               = (1²+2²+3²+....11²+12²+13²+14²+ ......, +23²)-(1²+2²+3²+....11²)
                                             
                                               = (1²+2²+3²+ ......, +23²)-(1²+2²+3²+....11²)
            
                                             = [23(23+1)(23x2+1)]/6 - [11(11+1)(11x2+1)]/6         [ using sum of square of natural number                                                                                                                                                 = n(n +1)(2n+1)/6 ]

                                              = [23x24x47]/6-[11x12x23]/6
                                             
                                              = 4324-506 = 3818 cm²

Hence total area of 12 square is 3818 cm²

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