Question

ABC is a right angled at B with $BC=6$ and $AC=10cm$. Also $△ABC$ and $△BCD$ are on the same base $BC$. Find $ar\left(△BCD\right)$.

• A. $12c{m}^2$
• B. $24c{m}^2$
• C. $6c{m}^2$
• D. $48c{m}^2$

Answer 1

The correct option is B $24c{m}^2$

Since $△ABC$ and $△BCD$ are on same base $BC$ and between same parallel lines, therefore,
$ar\left(△ABC\right)=ar\left(△BCD\right)$

$AB=\sqrt{{10}^2-6^2}=8cm$
$\frac{1}{2}\times 6\times 8=ar\left(△BCD\right)$
$\Rightarrow ar\left(△BCD\right)=24c{m}^2$