$1681.56 cm^2$
Hexagon Area Calculation
The problem asks for the area of a regular hexagon given its side length.
Given:
- Shape: Regular Hexagon
- Side length, \(s = 18\sqrt{2}\) cm
- Approximation: \(\sqrt{3} \approx 1.73\)
Area Formula for Regular Hexagon
The formula for the area (\(A\)) of a regular hexagon with side length \(s\) is:
\(A = \frac{3\sqrt{3}}{2} s^2\)
Step-by-Step Calculation
-
First, calculate the square of the side length (\(s^2\)):
\(s^2 = (18\sqrt{2})^2 = 18^2 \times (\sqrt{2})^2\)
\(s^2 = 324 \times 2 = 648 \text{ cm}^2\)
-
Now, substitute \(s^2\) into the area formula:
\(A = \frac{3\sqrt{3}}{2} \times 648\)
-
Simplify the expression:
\(A = 3\sqrt{3} \times \frac{648}{2}\)
\(A = 3\sqrt{3} \times 324\)
\(A = 972\sqrt{3} \text{ cm}^2\)
-
Use the given approximation for \(\sqrt{3}\) (\(\sqrt{3} \approx 1.73\)):
\(A \approx 972 \times 1.73\)
-
Perform the final multiplication:
\(A \approx 1681.56 \text{ cm}^2\)
Conclusion
The area of the regular hexagon is approximately \(1681.56\) cm\(^2\). This matches Option A.
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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 = \(\frac{22}{7}\))
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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 = \(\frac{22}{7}\))
