$1681.56 cm^2$
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
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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.
Similar Questions
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Important Questions from Mensuration
- The volume of a wall that is 5 times as high as it is broad and 8 times as long as it is high is 12.8 cubic meters. Find the breadth of the wall.
- If the radius of a sphere is increased by 2 cm, then its surface area increases by 704 cm\(^2\). Using \(\pi = \frac{22}{7}\), find the radius of the sphere after the increase.
- What is the perimeter of an equilateral triangle with side 13 cm?
- The perimeter of a square is 76 m. Its area (in $m^2$) is:
- A cylindrical rod has an outer curved surface area of 1800 cm$^2$. If the length of the rod is 52 cm, then the outer radius (in cm) of the rod, correct to two places of decimal, is:
Take $\pi = \frac{22}{7}$
