If the sum of the diagonals of a rhombus is L and the perimeter is 4P, find the area of the rhombus?

Answer: Option B

Sum of diagonal of quadrilateral = L
Perimeter = 4P
$$\begin{array}{rl}& {\left(\frac{\text{Diagonal}}{2}\right)}^2-{\left(\frac{\text{Semi perimeter}}{2}\right)}^2\\ & =\frac{{\text{L}}^2}{4}-{\left(\frac{2\text{P}}{2}\right)}^2\\ & =\frac{{\text{L}}^2}{4}-{\text{P}}^2\\ & =\frac{1}{4}\left({\text{L}}^2-4{\text{P}}^2\right)\end{array}$$