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(A) Let the original diagonal of the square be $d$.The area of a square in terms of its diagonal is given by the formula: $	ext{Area} = \frac{1}{2} d

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Becomes $4$-fold

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(A) Let the original diagonal of the square be $d$.The area of a square in terms of its diagonal is given by the formula: $	ext{Area} = \frac{1}{2} d^2$.Original area $A_1 = \frac{1}{2} d^2$.If the diagonal is doubled,the new diagonal $d' = 2d$.New area $A_2 = \frac{1}{2} (d')^2 = \frac{1}{2} (2d)^2 = \frac{1}{2} (4d^2) = 2d^2$.Comparing the new area with the original area:$A_2 = 4 	imes (\frac{1}{2} d^2) = 4 A_1$.Therefore,the area of the square becomes $4$-fold.

If a diagonal of a square is doubled,how does the area of the square change?

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