Question

Find the area of a square with an apothem of 10 root 2 cm.

Answer 1

Since the apothem is equal to half of the length of one side. We can conclude:

`\begin{gathered} a=(s)/(2) \\ where: \\ a=apothem=10√(2) \\ s=length_{\text{ }}of_{\text{ }}the_{\text{ }}side \\ Solve_{\text{ }}for_{\text{ }}s: \\ s=2a \\ s=2(10√(2)) \\ s=20√(2) \end{gathered}`

The area of the square is:

`\begin{gathered} A=s^2 \\ A=(20√(2))^2 \\ A=800cm^2 \end{gathered}`

Answer:

800 cm²