Volume of Triangular Pyramid Worksheet for 9th - 10th Grade ... - Free Printable

It looks like you've uploaded a worksheet titled "Volume of Triangular Pyramid", which contains several problems asking for the volume of triangular pyramids (also known as tetrahedrons). However, I can't view images directly. But based on your description and typical structure of such worksheets, I can help you solve the problems if you provide the specific values.

But since I can't see the image, let me explain how to solve volume of a triangular pyramid problems in general, and then you can apply it to your worksheet.

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🔷 Formula for Volume of a Triangular Pyramid:

$$
V = \frac{1}{3} \times \text{Base Area} \times \text{Height}
$$

Where:
- Base Area is the area of the triangular base:
$$
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height of triangle}
$$
- Height is the perpendicular height from the apex of the pyramid to the base.

So overall:
$$
V = \frac{1}{3} \times \left( \frac{1}{2} \times b \times h_{\text{triangle}} \right) \times H
$$
Where:
- $ b $ = base of the triangle
- $ h_{\text{triangle}} $ = height of the triangle (within the base)
- $ H $ = height of the pyramid (from apex to base)

Or simplified:
$$
V = \frac{1}{6} \times b \times h_{\text{triangle}} \times H
$$

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✔ Example Problem:

Let’s say one problem says:
> Length = 5 m, width = 4 m, height = 6 m

Wait — this terminology is ambiguous. In a triangular pyramid, "length", "width", and "height" might refer to:
- The base of the triangle (say, length = 5 m),
- The height of the triangle (say, width = 4 m),
- The height of the pyramid (say, 6 m).

So assuming:
- Base of triangle = 5 m
- Height of triangle = 4 m
- Height of pyramid = 6 m

Then:
$$
\text{Base Area} = \frac{1}{2} \times 5 \times 4 = 10 \, \text{m}^2
$$
$$
V = \frac{1}{3} \times 10 \times 6 = 20 \, \text{m}^3
$$

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📝 How to Solve Each Box on Your Worksheet:

Each box likely gives three numbers: length, width, height. You need to interpret them as:
- Length: base of the triangular face
- Width: height of the triangle (perpendicular to base)
- Height: height of the pyramid (from tip to base)

Then use:
$$
V = \frac{1}{3} \times \left( \frac{1}{2} \times \text{length} \times \text{width} \right) \times \text{height}
$$

Or:
$$
V = \frac{1}{6} \times \text{length} \times \text{width} \times \text{height}
$$

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🔍 Let's Try One Together (Example):

Suppose a box says:
> Length = 8 m, width = 3 m, height = 10 m

Then:
$$
V = \frac{1}{6} \times 8 \times 3 \times 10 = \frac{240}{6} = 40 \, \text{m}^3
$$

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🛠️ Step-by-step Instructions for You:

For each box:
1. Identify:
- Base of triangle = length
- Height of triangle = width
- Height of pyramid = height
2. Compute base area: $ \frac{1}{2} \times \text{length} \times \text{width} $
3. Multiply by pyramid height: $ \text{Base Area} \times \text{height} $
4. Divide by 3: $ V = \frac{1}{3} \times (\text{Base Area}) \times \text{height} $

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💡 Tip:

Make sure all units are consistent (e.g., all in meters), and write the final answer with correct units (e.g., m³).

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❗ Please Provide the Numbers

Since I can't see your image, please type out the values from each box (e.g., "Length = 6 m, width = 4 m, height = 9 m") and I’ll compute the volume for each one.

Or, if you describe the exact values, I’ll solve them step by step.

Let me know!