Question

Find the area of a quadrilateral one of whose diagonals is $30$ cm long and the perpendiculars from the two other vertices on this diagonal are $19$ cm and $11$ cm respectively.

• A. $450$ cm${}^2$
• B. $540$ cm${}^2$
• C. $320$ cm${}^2$
• D. $350$ cm${}^2$

Answer 1

The correct option is A $450$ cm${}^2$

$ABCD$ be the given quadrilateral $BE\perp AC$ and $DF\perp AC$
Let $AC=30m$
$BE=19m$ and
$DF=11m$
Area of quadrilateral $ABCD=$ Area of $△$ $ABC+$ Area of $△$ $ACD$
$=\frac{1}{2}\times AC\times BC+\frac{1}{2}\times AC\times DF$

$=\frac{1}{2}\times 30\times 19+\frac{1}{2}\times 30\times 11$

$=\frac{1}{2}\times 30\times 19+\frac{1}{2}\times 30\times 11$$=450c{m}^2$