Question

Find the area of a quadrilateral piece of ground, one of whose diagonals is $60$ metres long and the perpendiculars from the other two vertices are $38$ and $22$ metres, respectively.

• A. $1800m^2$
• B. $3600m^2$
• C. $900m^2$
• D. None of the above

Answer 1

The correct option is A $1800m^2$

We know that the area of a quadrilateral is equal to the product of one diagonal and half the sum of perpendiculars drawn on it from other two vertices.
$\Rightarrow$ Area of a quadrilateral $=\frac{1}{2}\times diagonal\times (p_1+p_2)$

where, $p_1$ and $p_2$ are two perpendiculars drawn from opposite vertices$
Given, length of one diagonal is $60m$ and the perpendiculars from the other two vertices are $38m$ and $22m$, respectively.
$⟹$ Area of the quadrilateral $=\frac{1}{2}\times 60\times (38+22)m^2=1800m^2$