Q. 55.0( 1 Vote )

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

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