Question

find the number of squares and rectangles in chess board of 8 x 8​

Answer 1

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Given:

Chess board of 8 x 8 tiles

Formula

$Number \: of\:Squares = \sum\limits^{n}_{r=1} r^2 \\ \implies \boxed{\dfrac{n(n+1)(2n+1)}{6}}$

$Number\:of\:rectangles = ^{n+1}C_2 \times ^{n+1}C_2$

SoluTion

Number of squares in 8 x 8 tiles

$\dfrac{n(n+1)(2n+1)}{6} \\ \implies \dfrac{8(8+1)(2\times8+1)}{6} \\ \implies \dfrac{8\times 9 \times 17}{6} \\ \implies 12\times 17 \\ \implies \boxed{204}$

Number of Rectangles

^{8+1}C_2 \times ^{8+1}C_2 \\ \implies \dfrac{9\times 8 }{2} \times \dfrac{9\times8}{2} \\ \implies 36 \times 36 \boxed{1296}[/tex]

Answer 2

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find the number of squares and rectangles in chess board of 8 x 8

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refer to the attachment

hope it helps you