Question

The circumradius of an equilateral triangle is x cm The area of the triangle in terms of X is _____ (in cm${}^2$)

• A. $\frac{3\sqrt{3}}{2}{x}^2$
• B. $\frac{3\sqrt{3}}{4}{x}^2$
• C. $\frac{4\sqrt{3}}{5}{x}^2$
• D. $\frac{5\sqrt{3}}{4}{x}^2$

Answer 1

The correct option is B $\frac{3\sqrt{3}}{4}{x}^2$

Circumradius of an equilateral triangle of side $a$ is given by $\frac{a}{\sqrt{3}}$
Given, $x=\frac{a}{\sqrt{3}}$
$=>a=\sqrt{3}x$
Area of an equilateral triangle with length of side $a=\frac{\sqrt{3}}{4}{a}^2=\frac{\sqrt{3}}{4}{\left(\sqrt{3}x\right)}^2=\frac{3\sqrt{3}}{4}{x}^2$