Question

ABCD is a trapezium in which AB || DC. If $ar\left(△ABD\right)=24c{m}^2$ and AB = 8 cm, then height of$△ABC$ is

• A. 3 cm
• B. 4 cm
• C. 6 cm
• D. 8 cm

Answer 1

The correct option is C

6 cm

In trapezium ABCD, AB || DC

AC and BD are joined
$ar\left(△ABD\right)=24c{m}^{2}AB=8cm$

$\because ar\left(△ABD\right)=\frac{1}{2}base\times altitude=\frac{1}{2}AB\times DM24=\frac{1}{2}\times 8\times DM\Rightarrow DM=\frac{24\times 2}{8}=6cm$
But DM = CL
$\therefore$ Height of $△ABC=6cm$