Question

The area of the $\Delta ABC$ equals .

• A. $\frac{1}{2}\left(c\times d\right)\mathrm{sq}.\mathrm{units}$
• B. $\frac{1}{2}\left(a\times d\right)\mathrm{sq}.\mathrm{units}$
• C. $\frac{1}{2}\left(b\times d\right)\mathrm{sq}.\mathrm{units}$

Answer 1

The correct option is A $\frac{1}{2}\left(c\times d\right)\mathrm{sq}.\mathrm{units}$


For the $\Delta ABC$, we have $AB=a;BC=b;CA=c\&d$ is the perpendicular from the vertex $B$.
Now, we know that the area of a triangle $=\frac{1}{2}\times \text{Base}\times \text{Height}$.
Now, here we have to select the appropriate Base and Height for the triangle.
Here, the perpendicular drawn on $AC$ from the vertex $B$ has a length $d$.
$\Rightarrow$ Correspondingly the Base will be $AC$
$\therefore$ The area of the $\Delta ABC$
$=\frac{1}{2}\times d\times c$ sq. units