Question

Find the area of a quadrilateral which has one of its diagonals as $10$ cm and the lengths of the perpendiculars drawn from the vertices to it are $3$ cm and $5$ cm (in $c{m}^2$).

• A. $25$
• B. $36$
• C. $40$
• D. $32$

Answer 1

The correct option is C $40$

Given that:

$AC=10cm,DM=3cm,D{M}^{\prime }=5cm$

To find:

Area of the quadrilateral $=?$

Solution:

Area of the quadrilateral $=$ Area of the $△ADC+$ Area of the $△ABC$

$=\frac{1}{2}\times DM\times AC+\frac{1}{2}\times D{M}^{\prime }\times AC$

$=\frac{1}{2}\times 3cm\times 10cm+\frac{1}{2}\times 5cm\times 10cm$

$=15c{m}^2+25c{m}^2$

$=40c{m}^2$

$\therefore$ Area of the quadrilateral $=40c{m}^2$

Hence, C is the correct option.