Answer
24 $m^{2}$
Work Step by Step
Find the length of the other diagonal by using the Pythagorean Theorem. Create a triangle cutting the diagonal given in half. This gives you a base to your triangle of 3.
$a^{2}$+$b^{2}$=$c^{2}$
$3^{2}$+$b^{2}$=$5^{2}$
9 + $b^{2}$=25
$b^{2}$=16
b=4
The diagonal is twice this length. 4x2=8
We use the formula for the area of a rhombus to obtain:
A=$\frac{1}{2}$($d_{1}$)($d_{2}$)
A=$\frac{1}{2}$(8)(6)
A=24
