Hexagon Area Calculation
Given Information
- Shape: Regular Hexagon
- Side Length ($a$): $2\sqrt{3}$ cm
Area Formula
The area of a regular hexagon with side length '$a$' is calculated using the formula:
Area = $\frac{3\sqrt{3}}{2} a^2$
Calculation Steps
- Calculate the square of the side length ($a^2$):
Given $a = 2\sqrt{3}$ cm.
$a^2 = (2\sqrt{3})^2 = 2^2 \times (\sqrt{3})^2 = 4 \times 3 = 12$ cm$^2$.
- Substitute $a^2$ into the area formula:
Area = $\frac{3\sqrt{3}}{2} \times 12$ cm$^2$.
- Simplify to find the area:
Area = $3\sqrt{3} \times \frac{12}{2}$ cm$^2$.
Area = $3\sqrt{3} \times 6$ cm$^2$.
Area = $18\sqrt{3}$ cm$^2$.
Conclusion
The calculated area of the regular hexagon is $18\sqrt{3}$ cm$^2$. This matches Option 3.
Similar Questions
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Important Questions from Plane Figures
If length of a rectangle is increased to its three times and breadth is decreased to its half, then the ratio of the area of given rectangle to the area of new rectangle is:
The width of the path around a square field is 4.5 m and its area is 105.75 m 2. Find the cost of fencing the field at the rate of Rs. 100 per meter.
What is the area of the square (in cm 2) whose vertices lie on a circle of radius 5 cm?
The circumcentre of an equilateral triangle is at a distance of 3.2 cm from the base of the triangle. What is the length (in cm) of each of its altitudes?
The perimeter of a circular lawn is 1232 m. There is 7 m wide path around the lawn. The area (in m 2) of the path is:
Take \(\left(\pi=\frac{22}{7}\right)\)
