Question

Find the area of the quadrilateral with diagonal $13m$and offsets $7m$ and $3m.$

Answer 1

Solve for area of the given quadrilateral

Given,

1. Length of the diagonal $d=13m.$
2. Offsets i.e. perpendiculars distances from opposite vertices to the diagonal, $h_1$and $h_2$ are $7m$ and $3m$respectively.

We know that, area of quadrilateral$\mathbf{=}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{\times }\mathit{d}\mathbf{\times }\left(h_1+h_2\right)$

$\therefore$ Area of the given quadrilateral $=\frac{1}{2}\times 13\times \left(7+3\right)$

$$\begin{gathered} =\frac{1}{2}\times 13\times 10 \\ =65m^2 \end{gathered}$$

Hence, the area of the quadrilateral is $65m^2$