Question

D is the mid-point of side BC of $\Delta ABC$ and E is the mid point of BD. If O is the midpoint of AE, then area of ($\Delta BOE$) is equal to

• A. $\frac{1}{8}$ Area ($\Delta$ ABC)
• B. $\frac{1}{6}$ Area ($\Delta$ ABC)
• C. $\frac{1}{4}$ Area ($\Delta$ ABC)
• D. $\frac{1}{3}$ Area ($\Delta$ ABC)

Answer 1

The correct option is A

$\frac{1}{8}$ Area ($\Delta$ ABC)

Since AD is the median,
$\therefore$2 ar $\Delta ABD)$ = ar $\Delta ABC)$ . . . . (i)
Similarly, 2 ar $\Delta ABE)$ = ar $\Delta ABD)$ . . . . (ii)
And 2 ar $\Delta BOE)$ = ar $\Delta ABE)$ . . . . (iii)
Now, ar $\Delta ABC)$ = 2ar $\Delta ABD)$
= 2[2ar $\Delta ABE\left)\right]$
= 4[2ar $\Delta BOE\left)\right]$
= 8 ar $\Delta BOE)$
$\therefore \frac{1}{8}$ ar $\Delta ABC)$ = ar $\Delta BOE)$