Question

Question 1
Write True or False and justify your answer :
ABCD is a parallelogram and X is the mid - point of AB. If ar (AXCD) = $24c{m}^2$, then ar (ABC) = $24c{m}^2$

Answer 1

False.
Given, ABCD is a parallelogram and ar (AXCD) = $24c{m}^2$
Let area of the parallelogram ABCD is 2y $c{m}^2$.
Join AC.

We know that, diagonal divides the area of parallelogram in two equal areas.
$\therefore$ ar (ABC) = ar (ACD) = y
So, ar (ACX) = ar (BCX) [since, x is median in $△$ABC]
$=\frac{1}{2}ar\left(ABC\right)=\frac{1}{2}y$
Now, ar (AXCD) = ar (ADC) + ar (ACX)
$24=y+\frac{y}{2}$
$\Rightarrow 24=\frac{3y}{2}$
$\Rightarrow ar\left(\Delta ABC\right)=16c{m}^2$
Therefore, given statement is false.