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

Given that there are 12 squares,

We see that their sides 12cm, 13cm..,23cm are in series.

To find the total area, we know that the area of a square is simply l² where l is the length of the side.

Area of first square = 12cm × 12cm = 12² cm²

Area of the second square = 13cm × 13cm = 13² cm²

And so on.

We observe that this is in a series.

So S = 12² + 13² + 14² + … + 23²

To find S,

Let S₁ be 1² + 2² + …. + 23² with n = 23

Let S₂ be 1² + 2² + …. + 11² with n = 11

S = S₁-S₂

To find S₁

1² + 2² + …. + 23² with n = 23

Formula to find the sum of first n squares of natural numbers is

S =

S₁ =

=

S₁ = 4324

To find S₂

1² + 2² + …. + 11² with n = 11

Formula to find the sum of first n squares of natural numbers is

S =

S₂ =

=

S₂ = 506

S = S₁-S₂

S = 4324-506

S = 3818cm²

The required sum S = 12² + 13² + 14² + … + 23² = 3818cm²