Question

ABCD is a parallelogram and L is the mid point of CD. If Ar (ABCL) = 72 cm${}^2$, then find Ar (ADC).

• A. 72 cm${}^2$
• B. 144 cm${}^2$
• C. 48 cm${}^2$
• D. 36 cm${}^2$

Answer 1

The correct option is C 48 cm${}^2$

Given, Ar (ABCL) = 72 cm${}^2$ and L is mid point of CD. So, CL = LD

Ar (ABCL) = 72 cm${}^2$
$\Rightarrow$ Ar (ABC) + Ar (ACL) = 72 cm${}^2$
$\because$ Median divides triangle into two equal halves
$\therefore$ Ar (ACL) = Ar (ALD) = $\frac{1}{2}\times$ Ar (ADC)
$\Rightarrow$ Ar (ABC) + $\frac{1}{2}\times$ Ar (ADC) = 72 cm${}^2$
$\because$ Diagonal of a parallelogram divides it into two triangles of equal areas.
$\therefore$ Ar (ABC) = Ar (ADC)
$\Rightarrow$ Ar (ADC) + $\frac{1}{2}\times$ Ar (ADC) = 72 cm${}^2$
$\Rightarrow$ $\frac{3}{2}\times$ Ar (ADC) = 72 cm${}^2$
$\Rightarrow$ Ar (ADC) = 48 cm${}^2$