Question

The area of the triangle formed by the points $A(2,3,4)$ , $B(3,4,2)$ and $C(4,2,3)$ is

• A. $3\sqrt{3}$
• B. $\frac{3\sqrt{3}}{2}$
• C. $\frac{\sqrt{3}}{2}$
• D. $\frac{5\sqrt{3}}{2}$

Answer 1

Answer: (B)

$\frac{3\sqrt{3}}{2}$

As all side are same so its on equilateral $\Delta$

Area of equilateral $\Delta =\frac{\sqrt{3}}{4}{a}^2$

$=\frac{\sqrt{3}}{4}\times 6$

$=\frac{3\sqrt{3}}{2}$