Since the apothem is equal to half of the length of one side. We can conclude:
[tex]\begin{gathered} a=\frac{s}{2} \\ where: \\ a=apothem=10\sqrt{2} \\ s=length_{\text{ }}of_{\text{ }}the_{\text{ }}side \\ Solve_{\text{ }}for_{\text{ }}s: \\ s=2a \\ s=2(10\sqrt{2}) \\ s=20\sqrt{2} \end{gathered}[/tex]
The area of the square is:
[tex]\begin{gathered} A=s^2 \\ A=(20\sqrt{2})^2 \\ A=800cm^2 \end{gathered}[/tex]
Answer:
800 cm²
