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Calculate the area of a regular hexagon with a side length of 20 cm.

Mathematics

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Answer

1039.2 cm21039.2 \text{ cm}^2

Step-by-step solution

4 steps
  1. Identify the shape and given dimensions.

    The road sign is in the shape of a regular hexagon.
    The side length of the hexagon is s=20s = 20 cm.

  2. State the formula for the area of a regular hexagon.

    The area AA of a regular hexagon with side length ss is given by the formula:

    A=332s2A = \frac{3\sqrt{3}}{2} s^2
  3. Substitute the given side length into the formula.

    Substitute s=20s = 20 cm into the formula:

    A=332(20)2A = \frac{3\sqrt{3}}{2} (20)^2
  4. Calculate the area.

    First, calculate 20220^2:

    A=332(400)A = \frac{3\sqrt{3}}{2} (400)

    Multiply 332\frac{3\sqrt{3}}{2} by 400:

    A=33×4002A = 3\sqrt{3} \times \frac{400}{2} A=33×200A = 3\sqrt{3} \times 200 A=6003 cm2A = 600\sqrt{3} \text{ cm}^2

    To provide a numerical value, use 3≈1.732\sqrt{3} \approx 1.732:

    A≈600×1.732A \approx 600 \times 1.732 A≈1039.2 cm2A \approx 1039.2 \text{ cm}^2

    The area of the road sign is approximately 1039.2 cm2^2.

    1039.2 cm21039.2 \text{ cm}^2
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