# If the area of a square is 12cm^2 what is the product of its diagonals?

Jun 25, 2015

The product of the diagonals of a square with area $12 c {m}^{2}$ is $24 c m$

#### Explanation:

If the area of a square is 12
each side has a length of $\sqrt{12}$

The product of the diagonals is the same as the square of a diagonal (since the diagonals of a square are equal in length).

By the Pythagorean Theorem:
the square of a diagonal = sum of the squares of the two sides
$\textcolor{w h i t e}{\text{XXXX}}$$= {\left(\sqrt{12}\right)}^{2} + {\left(\sqrt{12}\right)}^{2}$

$\textcolor{w h i t e}{\text{XXXX}}$$= 24$