Question

A diagonal of a quadrilateral is $26cm$ and the perpendiculars drawn to it from the opposite vertices are $12.8cm$ and $11.2cm$. Find the area of the quadrilateral.

Answer 1

The quadrilateral with given measurements is

Given:- $AC=26cm$
$DL=12.8cm$
$BM=11.2cm$

Area of $△ACD=\frac{1}{2}\times AC\times DL=\frac{1}{2}\times 26\times 12.8=166.4{cm}^2$

Area of $△ABC=\frac{1}{2}\times AC\times BM=\frac{1}{2}\times 26\times 11.2=145.6{cm}^2$

Therefore,Area of quadrilateral $=ar\left(△ACD\right)+ar\left(△ABC\right)$

$=166.4+145.6=312{cm}^2$