Calculate Hexagon Side Length
A regular hexagon consists of 6 equal sides. The perimeter is the total length around the shape.
- Perimeter = 6 × side length (s)
- Given Perimeter = 72 cm
- Therefore, $72 \text{ cm} = 6 \times s$
- Solving for the side length: $s = \frac{72 \text{ cm}}{6} = 12 \text{ cm}$
Calculate Regular Hexagon Area
The standard formula to find the area of a regular hexagon using its side length (s) is:
Area = $\frac{3\sqrt{3}}{2} s^2$
Substitute the calculated side length, s = 12 cm, into the area formula:
- Area = $\frac{3\sqrt{3}}{2} (12 \text{ cm})^2$
- Area = $\frac{3\sqrt{3}}{2} \times 144 \text{ cm}^2$
- Area = $3\sqrt{3} \times \frac{144}{2} \text{ cm}^2$
- Area = $3\sqrt{3} \times 72 \text{ cm}^2$
- Area = $216\sqrt{3} \text{ cm}^2$
Approximate Area Value
To find the numerical value, use the approximation $\sqrt{3} \approx 1.732$:
Area $\approx 216 \times 1.732 \text{ cm}^2$
Area $\approx 374.112 \text{ cm}^2$
Rounding to two decimal places, the area is approximately $374.12 \text{ cm}^2$.
Similar Questions
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Important Questions from Mensuration
In a circular garden of radius 15 m, a path of 2 m wide has to be made inside the garden at the rate of ₹ 24 per sq. m. The cost of making the path is: (Take π = \(\frac{22}{7}\) )
A hollow cylinder with outer radius 4 cm and height 2 cm is made up of 1 cm thick metal sheet. What is the volume of metal used? (Take π = \(\frac{22}{7}\))
The length and breadth of a rectangular field are in the ratio 4 : 3. If the cost of cultivating the field at ₹2 per m 2is ₹600, then the length of the field is:
A cylindrical tank has a capacity of 5632 m3. If the diameter of its base is 8 m, what is the depth of the cylindrical tank? (Use π = \(\frac{22}{7}\))
Find the surface area of a sphere whose diameter is equal to 28 cm.
