Find the area the quadrilateral LMNOP (as shown in the figure).

Solution

Diagonal LN = 8 cm
Perpendicular MX = 4.5 cm
Perpendicular OY = 3.5 cm
∵ Sum of the perpendiculars = MX + OY = 4.5 cm + 3.5 cm = 8 cm
∴ Area of the quadrilateral = $1 half cross times$ (A diagonal ) x (Sum of the lengths of the perpendiculars on it from opposite vertices)
$equals 1 half cross times space 8 space cross times space 8 space cm squared space equals space 32 space cm squared$