Question

If the length of each side of an equilateral triangle is equal to the radius of a circle of area 154 sq. cm., then the area of the equilateral triangle is

• A. $\frac{7\sqrt{3}}{4}$sq. cm
• B. $\frac{49\sqrt{3}}{4}$sq. cm
• C. $35$ sq. cm
• D. $49$sq. cm

Answer 1

The correct option is B $\frac{49\sqrt{3}}{4}$sq. cm

If $r$ is the radius of the circle, then
Area of circle $\pi r^2=154$
$\therefore r^2=\frac{154\times 7}{22}\times 7^2$
$\therefore r=7$ cm
Area of the equilateral triangle with side 7 cm,
$A=7^2\times \frac{\sqrt{3}}{4}$
$=\frac{49\sqrt{3}}{4}$ sq. cm.