Note: The diagonals of a rhombus bisect each other at right angle
[tex]\begin{gathered} \text{ The area of a rhombus = }\frac{1}{2}\text{ x d1 x d2} \\ \text{where d1 and d2 are the lengths of the two diagonals} \end{gathered}[/tex]We need to calculate the length of the other diagonal, that is diagonal AC.
E is the midpoint of AC
We can use the Pythagoras theorem to find the value of m
[tex]\begin{gathered} \text{ In }\Delta BEC,\text{ } \\ 8^2=4^2+m^2 \\ m^2=8^2-4^2 \\ m^2=64-16 \\ m^2=48 \\ m=\sqrt[]{48} \\ m=4\sqrt[]{3}\text{ in} \\ \text{But diagonal }AC\text{ = 2 x m = 2 x 4}\sqrt[]{3\text{ }}=8\sqrt[]{3}\text{ in} \end{gathered}[/tex][tex]\begin{gathered} \text{ Area of the rhombus = }\frac{1}{2}\text{ x AC x BD} \\ =\frac{1}{2}\text{ x 8}\sqrt[]{3}\text{ x 8} \\ =32\sqrt[]{3}in^2\text{ } \\ or\text{ in decimal} \\ \text{Area = 55.43 in}^2 \end{gathered}[/tex]
