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

It is given that, 
Length of the diagonal, d = 24 m 
Length of the perpendiculars, h₁ and h₂, from the opposite vertices to the diagonal are h₁ = 8 m and h₂ = 13 m 
Area of the quadrilateral
\(= \frac{1}{2}(\text{ dh}_1)+ \frac{1}{2}(\text{dh}_2)\)

\(= \frac{1}{2}\) \(\times\)\(\text{d(h}_1+\text{h}_2)\)

\(= \frac{1}{2}\)×24×(13+8)

\(= \frac{1}{2}\)×24×21 = 252

Hence, the required area of the field is 252 m²