Area and Perimeter Practice Test 2

Suppose side of the square = x cm
∴ Diagonal of the square = 2 x cm.
And area of the square = ${\mathit{x}}^2$ cm, i.e., $\frac{{\left(\mathrm{Diagonal}\right)}^2}{2}$
Diagonal of the new square = 2 × $\sqrt{2}\mathit{x}$ = $2\sqrt{2\mathit{x}}$ cm.
∴ Area of the new square = $\frac{{\left(\mathrm{Diagonal}\mathrm{of}\mathrm{the}\mathrm{new}\mathrm{square}\right)}^2}{2}$
= $\frac{{\left(2\sqrt{2}\mathit{x}\right)}^2}{2}$
= $4{\mathit{x}}^2$ sq. cm.
Thus area of the new square will become fourfold.