Question

If ABCDEF is a regular hexagon with each side equal to 6 cm and the distance of the circumcentre from any of the sides is 4 cm, then it's area is .

• A. $64c{m}^2$
• B. $72c{m}^2$
• C. $59c{m}^2$

Answer 1

The correct option is B $72c{m}^2$

Since, it is a regular hexagon, the triangles formed by its diagonals will have equal area.
So, in $△AOB$
$base=6cm$
$height=4cm$
$\text{Area}=\frac{1}{2}\times base\times height$
$\text{Area}=\frac{1}{2}\times 6\times 4=12c{m}^2$

The total count of triangles in the above figure is 6.
Therefore, the area of the hexagon ABCDEF is
$=6\times 12c{m}^2=72c{m}^2$