Q. 55.0( 1 Vote )

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

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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