Calculate the Area of a Regular Hexagon with 8 cm Sides: Geometric Formula

Regular Hexagon Area with Known Side

A hexagon has sides measuring 8 8 cm long. What is the area of the hexagon?

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Step-by-step written solution

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1

Understand the problem

A hexagon has sides measuring 8 8 cm long. What is the area of the hexagon?

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Step-by-step solution

The formula to find the area of a regular hexagon with side length s s is given by:

332s2 \frac{3 \sqrt{3}}{2} s^2

For a hexagon with side length 8 cm 8 \text{ cm} , substitute s=8 s = 8 into the formula:

Area=332×82 \text{Area} = \frac{3 \sqrt{3}}{2} \times 8^2

Calculate 82 8^2 :

82=64 8^2 = 64

Substitute back:

Area=332×64 \text{Area} = \frac{3 \sqrt{3}}{2} \times 64

This simplifies to:

166.28 cm2 166.28 \text{ cm}^2

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Final Answer

166.28 cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = 332s2 \frac{3\sqrt{3}}{2} s^2 for regular hexagons
  • Technique: Square the side length first: 82=64 8^2 = 64
  • Check: Six triangular sections create the complete hexagon area ✓

Common Mistakes

Avoid these frequent errors
  • Using perimeter formula instead of area formula
    Don't calculate 6 × 8 = 48 cm² thinking this gives area! This only gives the perimeter. The area formula requires 332s2 \frac{3\sqrt{3}}{2} s^2 because a hexagon consists of six equilateral triangles. Always use the proper area formula with the coefficient 332 \frac{3\sqrt{3}}{2} .

Practice Quiz

Test your knowledge with interactive questions

A hexagon has sides measuring \( 8 \)cm long. What is the area of the hexagon?

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FAQ

Everything you need to know about this question

Why is the hexagon area formula so complicated?

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A regular hexagon is made of 6 equilateral triangles! Each triangle has area 34s2 \frac{\sqrt{3}}{4} s^2 , so multiply by 6 to get 332s2 \frac{3\sqrt{3}}{2} s^2 .

Do I need to memorize this formula?

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It helps! But you can also remember that a hexagon = 6 equilateral triangles. Find one triangle's area and multiply by 6.

What does 3 \sqrt{3} equal approximately?

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31.732 \sqrt{3} \approx 1.732 , so 3322.598 \frac{3\sqrt{3}}{2} \approx 2.598 . This gives us 2.598 × 64 ≈ 166.28 cm².

Can I use this formula for any hexagon?

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Only for regular hexagons! All sides must be equal and all angles must be 120°. Irregular hexagons need different methods.

How do I know if 166.28 cm² is reasonable?

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Compare to a square with 8 cm sides: 8² = 64 cm². A hexagon should be larger than this square, and 166.28 > 64, so it makes sense!

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