Question

In the given figure, if BD=DC, AP=PC and area $\Delta BPC=20c{m}^2,$ then area $\Delta ABD=$ ___$c{m}^2$

• A. 20
• B. 40
• C. 50
• D. 10

Answer 1

The correct option is A

20

BD=DC(given)

$\therefore AD$ is median of $\Delta ABC$

(ii)AP=PC (given)

$\therefore BP$ is median of $\Delta ABC$

(iii)area $\Delta ABC=2\times$ area $\Delta BPC$

$=2\times 20$

$=40c{m}^2$

(median divides a $\Delta$ into two ${\Delta }^{\prime }s$ of equal area)

$\left(iv\right)\therefore$ area $\Delta ABD=\frac{1}{2}$ area $\Delta ABC=\frac{1}{2}\times 40$

$=20c{m}^2$

Hence (A)