Calculate the Area of a Regular Hexagon with 10cm Sides

Q: Why can't I just multiply 6 × 10 to get the area?

That would give you the perimeter (60 cm), not the area! Area measures the space inside the shape in square units. You need the special hexagon formula: $ \frac{3\sqrt{3}}{2}s^2 $.

Q: What does the √3 in the formula represent?

The $ \sqrt{3} $ comes from the geometry of regular hexagons. It relates to the height of equilateral triangles that make up the hexagon. You can use $ \sqrt{3} \approx 1.732 $ for calculations.

Q: Can I break the hexagon into triangles instead?

Yes! A regular hexagon splits into 6 equilateral triangles. Find the area of one triangle using $ \frac{\sqrt{3}}{4}s^2 $, then multiply by 6. This gives the same result!

Q: How do I remember this formula?

Think: "3 square-root-3 over 2, times s-squared". The 3 represents the 6 triangles (6÷2=3), and $ \sqrt{3} $ comes from triangle height. Practice with different side lengths!

Q: What if my calculator doesn't have a square root button?

You can use $ \sqrt{3} = 1.732 $ as an approximation. So the formula becomes: $ \frac{3 \times 1.732}{2} \times s^2 = 2.598 \times s^2 $.

Regular Hexagon Area with Given Sides

A hexagon has sides measuring $10$ cm long. What is the area of the hexagon?

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Step-by-step written solution

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Understand the problem

A hexagon has sides measuring $10$ cm long. What is the area of the hexagon?

Step-by-step solution

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

$\frac{3 \sqrt{3}}{2} s^2$

For a hexagon with side length $10 \text{ cm}$ , substitute $s = 10$ into the formula:

$\text{Area} = \frac{3 \sqrt{3}}{2} \times 10^2$

Calculate $10^2$ :

$10^2 = 100$

Substitute back:

$\text{Area} = \frac{3 \sqrt{3}}{2} \times 100$

This simplifies to:

$259.81 \text{ cm}^2$

Final Answer

259.81 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Regular hexagon area is $\frac{3\sqrt{3}}{2}s^2$
Calculation: Substitute s=10: $\frac{3\sqrt{3}}{2} \times 100 = 259.81$
Check: Answer should be around 260 cm² for 10cm sides ✓

Common Mistakes

Avoid these frequent errors

Using wrong polygon area formula
Don't use triangle area formula (1/2 × base × height) or rectangle area (length × width) = completely wrong result! These formulas don't work for hexagons. Always use the specific regular hexagon formula: $\frac{3\sqrt{3}}{2}s^2$ .

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

Why can't I just multiply 6 × 10 to get the area?

That would give you the perimeter (60 cm), not the area! Area measures the space inside the shape in square units. You need the special hexagon formula: $\frac{3\sqrt{3}}{2}s^2$ .

What does the √3 in the formula represent?

The $\sqrt{3}$ comes from the geometry of regular hexagons. It relates to the height of equilateral triangles that make up the hexagon. You can use $\sqrt{3} \approx 1.732$ for calculations.

Can I break the hexagon into triangles instead?

Yes! A regular hexagon splits into 6 equilateral triangles. Find the area of one triangle using $\frac{\sqrt{3}}{4}s^2$ , then multiply by 6. This gives the same result!

How do I remember this formula?

Think: "3 square-root-3 over 2, times s-squared". The 3 represents the 6 triangles (6÷2=3), and $\sqrt{3}$ comes from triangle height. Practice with different side lengths!

What if my calculator doesn't have a square root button?

You can use $\sqrt{3} = 1.732$ as an approximation. So the formula becomes: $\frac{3 \times 1.732}{2} \times s^2 = 2.598 \times s^2$ .

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