Educational worksheet for calculating the volume of rectangular prisms and pyramids.

Problem Analysis:

The image contains a worksheet titled "Unit 6 Study Guide: Review Packet." It focuses on the Volume of Rectangular Prisms and Pyramids. The tasks involve calculating volumes for both rectangular prisms and pyramids, as well as identifying geometric properties.

Let's break down each part of the problem and solve it step by step.

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Part 1: Volume of Rectangular Prisms

#### Question 1:
- Task: Find the volume of the rectangular prism shown.
- Given: Dimensions of the rectangular prism are provided in the diagram (length = 4 ft, width = 3 ft, height = 2 ft).

#### Solution:
The formula for the volume of a rectangular prism is:
\[
V = \text{length} \times \text{width} \times \text{height}
\]
Substitute the given dimensions:
\[
V = 4 \, \text{ft} \times 3 \, \text{ft} \times 2 \, \text{ft} = 24 \, \text{cubic feet}
\]

#### Answer:
\[
\boxed{24 \, \text{cubic feet}}
\]

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Part 2: Volume of Pyramids

#### Question 2:
- Task: Find the volume of the triangular pyramid shown.
- Given: The base is a triangle with a base length of 5 cm and a height of 3 cm. The height of the pyramid is 4 cm.

#### Solution:
The formula for the volume of a pyramid is:
\[
V = \frac{1}{3} \times \text{Base Area} \times \text{Height of Pyramid}
\]

1. Calculate the area of the triangular base:
The formula for the area of a triangle is:
\[
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
Substitute the given values:
\[
\text{Base Area} = \frac{1}{2} \times 5 \, \text{cm} \times 3 \, \text{cm} = \frac{1}{2} \times 15 \, \text{cm}^2 = 7.5 \, \text{cm}^2
\]

2. Calculate the volume of the pyramid:
Substitute the base area and the height of the pyramid into the volume formula:
\[
V = \frac{1}{3} \times 7.5 \, \text{cm}^2 \times 4 \, \text{cm} = \frac{1}{3} \times 30 \, \text{cm}^3 = 10 \, \text{cm}^3
\]

#### Answer:
\[
\boxed{10 \, \text{cm}^3}
\]

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Part 3: Identifying Properties of Prisms and Pyramids

#### Question 3:
- Task: Identify the name of a polyhedron that has two parallel bases that are congruent polygons.
- Explanation:
A polyhedron with two parallel bases that are congruent polygons is called a prism. The type of prism depends on the shape of the bases (e.g., triangular prism, rectangular prism, etc.).

#### Answer:
\[
\boxed{\text{Prism}}
\]

#### Question 4:
- Task: Identify the name of a polyhedron that has one polygonal base and triangular faces that meet at a common vertex.
- Explanation:
A polyhedron with one polygonal base and triangular faces that meet at a common vertex is called a pyramid. The type of pyramid depends on the shape of the base (e.g., triangular pyramid, square pyramid, etc.).

#### Answer:
\[
\boxed{\text{Pyramid}}
\]

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Final Answers:

1. Volume of the rectangular prism: \(\boxed{24 \, \text{cubic feet}}\)
2. Volume of the triangular pyramid: \(\boxed{10 \, \text{cm}^3}\)
3. Polyhedron with two parallel congruent bases: \(\boxed{\text{Prism}}\)
4. Polyhedron with one polygonal base and triangular faces meeting at a vertex: \(\boxed{\text{Pyramid}}\)