Q. 55.0( 1 Vote )

# Find the total ar

Answer :

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 l^{2} where l is the length of the side.

Area of first square = 12cm × 12cm = 12^{2} cm^{2}

Area of the second square = 13cm × 13cm = 13^{2} cm^{2}

And so on.

We observe that this is in a series.

So S = 12^{2} + 13^{2} + 14^{2} + … + 23^{2}

To find S,

Let S_{1} be 1^{2} + 2^{2} + …. + 23^{2} with n = 23

Let S_{2} be 1^{2} + 2^{2} + …. + 11^{2} with n = 11

S = S_{1}-S_{2}

__To find S _{1}__

1^{2} + 2^{2} + …. + 23^{2} with n = 23

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

S =

S_{1} =

=

S_{1} = 4324

__To find S _{2}__

1^{2} + 2^{2} + …. + 11^{2} with n = 11

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

S =

S_{2} =

=

S_{2} = 506

__S = S _{1}-S_{2}__

S = 4324-506

S = 3818cm^{2}

The required sum S = 12^{2} + 13^{2} + 14^{2} + … + 23^{2} = 3818cm^{2}

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