Area of an Equilateral Triangle Worksheets - Free Printable

Since I can't view or access images directly, I can't see the specific details of your uploaded image. However, based on the text you've provided, it appears to be a worksheet titled "Area of an Equilateral Triangle" with several equilateral triangles labeled with side lengths and blank spaces for calculating their areas.

Let me walk you through how to solve this type of problem, and then I’ll guide you on how to apply it to each triangle in the worksheet.

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🔷 Formula for Area of an Equilateral Triangle

For an equilateral triangle with side length $ s $, the area is:

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

This formula comes from the general triangle area formula $ \frac{1}{2}bh $, using the height derived from the Pythagorean theorem.

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🔷 Step-by-Step Solution

1. Identify the side length $ s $ of each equilateral triangle.
2. Plug into the formula:
$$
\text{Area} = \frac{\sqrt{3}}{4} \times s^2
$$
3. Calculate:
- Square the side length.
- Multiply by $ \frac{\sqrt{3}}{4} $ (approx. $ 0.4330 $).
4. Round to two decimal places.

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Now, let's assume the side lengths given in the worksheet are as follows (based on typical problems like this):

> You mentioned:
> Example: $ s = 2.3 $ → Area ≈ $ 2.29 $ m²
> So we'll use that as a model.

Let’s suppose the side lengths for the problems are:

1) $ s = 20.1 $ ft
2) $ s = 12 $ cm
3) $ s = 8 $ mm
4) $ s = 15.6 $ in
5) $ s = 6.4 $ ft
6) $ s = 7.2 $ cm
7) $ s = 10 $ m
8) $ s = 12.5 $ ft
9) $ s = 15 $ cm

*(Note: These are hypothetical values — please adjust if your actual image has different numbers.)*

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✔ Let’s calculate each one:

#### 1) $ s = 20.1 $
$$
\text{Area} = \frac{\sqrt{3}}{4} \times (20.1)^2 = 0.4330 \times 404.01 \approx 174.72
$$
✔ Area ≈ 174.72 ft²

#### 2) $ s = 12 $
$$
\text{Area} = 0.4330 \times 144 = 62.352 \approx 62.35
$$
✔ Area ≈ 62.35 cm²

#### 3) $ s = 8 $
$$
\text{Area} = 0.4330 \times 64 = 27.712 \approx 27.71
$$
✔ Area ≈ 27.71 mm²

#### 4) $ s = 15.6 $
$$
\text{Area} = 0.4330 \times (15.6)^2 = 0.4330 \times 243.36 \approx 105.30
$$
✔ Area ≈ 105.30 in²

#### 5) $ s = 6.4 $
$$
\text{Area} = 0.4330 \times 40.96 \approx 17.70
$$
✔ Area ≈ 17.70 ft²

#### 6) $ s = 7.2 $
$$
\text{Area} = 0.4330 \times 51.84 \approx 22.42
$$
✔ Area ≈ 22.42 cm²

#### 7) $ s = 10 $
$$
\text{Area} = 0.4330 \times 100 = 43.30
$$
✔ Area ≈ 43.30 m²

#### 8) $ s = 12.5 $
$$
\text{Area} = 0.4330 \times 156.25 \approx 67.66
$$
✔ Area ≈ 67.66 ft²

#### 9) $ s = 15 $
$$
\text{Area} = 0.4330 \times 225 = 97.425 \approx 97.43
$$
✔ Area ≈ 97.43 cm²

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📝 Final Answer Format (for your worksheet):

| Problem | Side Length | Area (rounded to 2 decimals) |
|--------|-------------|-------------------------------|
| 1) | 20.1 ft | 174.72 ft² |
| 2) | 12 cm | 62.35 cm² |
| 3) | 8 mm | 27.71 mm² |
| 4) | 15.6 in | 105.30 in² |
| 5) | 6.4 ft | 17.70 ft² |
| 6) | 7.2 cm | 22.42 cm² |
| 7) | 10 m | 43.30 m² |
| 8) | 12.5 ft | 67.66 ft² |
| 9) | 15 cm | 97.43 cm² |

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💡 Tips:

- Always check units — make sure you're consistent.
- Use a calculator for $ \sqrt{3} \approx 1.732 $, so $ \frac{\sqrt{3}}{4} \approx 0.4330 $.
- Round only at the end.

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⚠️ If your actual image has different side lengths, please tell me the exact values (e.g., "Problem 1: side = 10 cm", etc.), and I’ll recalculate accordingly.

Would you like me to help you fill in the answers based on the actual numbers in your image? Just describe them!