Question

In the given figure, if ABCD is a parallelogram and E is the mid-point of BC, then area$\left(\Delta DEC\right)=k$ area(ABCD). Find k.

• A. $2$
• B. $\frac{1}{4}$
• C. $\frac{1}{2}$
• D. $\frac{2}{3}$

Answer 1

The correct option is B $\frac{1}{4}$

We Know that,

Area of $△DEC=\frac{1}{2}\times DE\times Height$

$\because DE=\frac{BC}{2}$ $\left[\because EisthemidpointofBC\right]$

So,

Area of $△DEC=\frac{1}{2}\times DE\times \times Height=\frac{1}{2}\times \frac{BC}{2}\times Height$

But,

$BC\times Height=Area\left(ABCD\right)$

$\therefore$ Area of $△DEC=\frac{1}{4}\times Area\left(ABCD\right)$