Question

In the figure given below, ABC is an equilateral triangle. D, E, F, G, H and I are the trisector points of the sides as shown. If the side of the triangle ABC is $6$cm, then the area of the regular hexagon DEFGHI is

• A. $3\sqrt{3}c{m}^2$
• B. $4\sqrt{3}c{m}^2$
• C. $5\sqrt{3}c{m}^2$
• D. $6\sqrt{3}c{m}^2$

Answer 1

The correct option is D $6\sqrt{3}c{m}^2$

Each side of hexagon $=\frac{1}{3}\times 6=2$cm
Area of hexagon $6\times \frac{\sqrt{3}}{4}(side{)}^2=6\times \frac{\sqrt{3}}{4}(2{)}^2$
$=6\times \frac{\sqrt{3}}{4}=4=6\sqrt{3}c{m}^2$