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