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 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

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