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 $374.12 \text{ cm}^2$.
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Important Questions from Mensuration
The areas of three adjacent faces of a cuboidal tank are 3 m 2, 12 m 2 and 16 m 2. the capacity of the tank, in litres, is:
Volume of a cuboid is 4800 cm 3. If the height of this cuboid is 20 cm, then what will be the area of the base of cuboid ?
Two similar cubes have heights of 8 cm and 12 cm, respectively. If the capacity of the smaller cube is 80 cm 3, what is the capacity of the bigger cube (in cm 3)?
Three circles of radius 7 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
Three circles of radius 6 cm are kept touching each other. The string is tightly tied around these three circles. What is the length of the string?
