Question

The diagonal of a quadrilateral shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. Find the area of the field.

Answer 1

Given: 

Diagonal of a quadrilateral shaped field = 24 m
Perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m.
Now, we know:
Area \[= \frac{1}{2} \times d \times ( h_1 + h_2 )\]
∴  Area of the field \[= \frac{1}{2} \times 24 \times (8 + 13)\]
\[ = 12 \times 21\]
\[ = 252 m^2\]