Area of Equilateral Triangle - Free Printable

It looks like you've uploaded an image of a worksheet titled "Area of an Equilateral Triangle 1 Answers", which provides the answers to six problems involving calculating the area of equilateral triangles. However, the task seems to be asking for a solution explanation rather than just the answers.

Let me walk through how to calculate the area of an equilateral triangle and verify each answer using the formula:

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🔷 Formula for Area of an Equilateral Triangle:

$$
\text{Area} = \frac{\sqrt{3}}{4} \times s^2
$$

Where:
- $ s $ is the length of one side of the equilateral triangle.

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Now let’s go through each problem and verify the given answers.

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✔ Problem 1:

- Side = 8 cm
- Area = ?

$$
\text{Area} = \frac{\sqrt{3}}{4} \times 8^2 = \frac{\sqrt{3}}{4} \times 64 = 16\sqrt{3} \approx 16 \times 1.732 = 27.712 \, \text{cm}^2
$$

✔ Answer: 27.7 cm² → Correct (rounded to 1 decimal place)

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✔ Problem 2:

- Side = 12 in
- Area = ?

$$
\text{Area} = \frac{\sqrt{3}}{4} \times 12^2 = \frac{\sqrt{3}}{4} \times 144 = 36\sqrt{3} \approx 36 \times 1.732 = 62.352 \, \text{in}^2
$$

✔ Answer: 62.4 in² → Correct (rounded to 1 decimal place)

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✔ Problem 3:

- Side = 6 cm
- Area = ?

$$
\text{Area} = \frac{\sqrt{3}}{4} \times 6^2 = \frac{\sqrt{3}}{4} \times 36 = 9\sqrt{3} \approx 9 \times 1.732 = 15.588 \, \text{cm}^2
$$

✔ Answer: 15.6 cm² → Correct (rounded to 1 decimal place)

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✔ Problem 4:

- Side = 2.5 m
- Area = ?

$$
\text{Area} = \frac{\sqrt{3}}{4} \times (2.5)^2 = \frac{\sqrt{3}}{4} \times 6.25 = 1.5625\sqrt{3} \approx 1.5625 \times 1.732 = 2.699 \, \text{m}^2
$$

✔ Answer: 2.7 m² → Correct (rounded to 1 decimal place)

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✔ Problem 5:

- Side = 6.2 m
- Area = ?

$$
\text{Area} = \frac{\sqrt{3}}{4} \times (6.2)^2 = \frac{\sqrt{3}}{4} \times 38.44 = 9.61\sqrt{3} \approx 9.61 \times 1.732 = 16.63 \, \text{m}^2
$$

✔ Answer: 16.6 m² → Correct (rounded to 1 decimal place)

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✔ Problem 6:

- Side = 8½ ft = 8.5 ft
- Area = ?

$$
\text{Area} = \frac{\sqrt{3}}{4} \times (8.5)^2 = \frac{\sqrt{3}}{4} \times 72.25 = 18.0625\sqrt{3} \approx 18.0625 \times 1.732 = 31.28 \, \text{ft}^2
$$

✔ Answer: 31.3 ft² → Correct (rounded to 1 decimal place)

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📌 Summary:

All the given answers are correct and have been properly rounded to one decimal place.

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🔍 Key Takeaway:

To find the area of an equilateral triangle:
1. Use the formula:
$$
A = \frac{\sqrt{3}}{4} \times s^2
$$
2. Plug in the side length.
3. Multiply by $ \sqrt{3} \approx 1.732 $ if needed.
4. Round appropriately.

This method works because all sides and angles are equal in an equilateral triangle, so the height can be derived using Pythagoras' theorem, leading to this simplified formula.

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If you were asked to solve these problems (not just check answers), then this step-by-step verification shows how each area was calculated.

Let me know if you'd like a printable version or practice problems! 😊