Question

Calcule a área deste quadrado :

Answer 1

$\textrm{A diagonal de um quadrado \'e dada}\\ \mathrm{por\ \mathbf{lado \times\sqrt{2}}.}\ \textrm{Portanto, se}\ \mathrm{d=5:}\\\\ \mathrm{d=5\ \to\ l\sqrt{2}=5\ \to\ l=\dfrac{5}{\sqrt{2}}}\\\\ \mathrm{l=\dfrac{5}{\sqrt{2}}\times\dfrac{\sqrt{2}}{\sqrt{2}}\ \to\ \boxed{\mathbf{l=\dfrac{5\sqrt{2}}{2}\ m}}}$

$\textrm{A \'area, por sua vez, \'e dada por}\\ \mathbf{lado^2.}\ \mathrm{Portanto,\ se\ l=5\sqrt{2}/2:}\\\\ \mathrm{A=l^2\ \to\ A=\bigg(\dfrac{5\sqrt{2}}{2}\bigg)^2}\\\\ \mathrm{A=\dfrac{25.2}{4}\ \to\ \boxed{\mathbf{A=\dfrac{25}{2}\ m^2}}}$