Solid geometry is concerned with three-dimensional shapes. In these lessons, we will learn

- what is a prism?
- how to find the volume of prisms.
- how to solve word problems about prisms.

**Related Pages**

Volume Formula

Volume Of Prism Worksheet

Volume Formulas Explained

More Geometry Lessons

A prism is a solid that has two parallel faces which are congruent polygons at both ends. These faces form the bases of the prism. A prism is named after the shape of its base.

The other faces are in the shape of parallelograms. They are called lateral faces.

The following diagrams show a triangular prism and a rectangular prism.

A right prism is a prism that has its bases perpendicular to its lateral surfaces. If the bases are not perpendicular to its lateral bases then it is called an oblique prism.

When we cut a prism parallel to the base, we get a cross section of a prism. The cross section has the same size and shape as the base.

**Example:**

**What is a prism and distinguishes between a right prism and an oblique prism?**

**How to label the parts of a prism and how to distinguish between an oblique and a right prism?**

The volume of a right prism is given by the formula:

**Volume = Area of base × height** = Ah

where A is the area of the base and h is the height or length of the prism.

Worksheet to calculate volume of prisms and pyramids.

**Example:**

Find the volume of the following right prism.

**Solution:**

Volume = Ah

= 25 cm^{2} × 9 cm

= 225 cm^{3}

**Example:**

Find the volume of the following right prism

**Solution:**

First, we need to calculate the area of the triangular base.

We would need to use Pythagorean theorem to calculate the height of the triangle.

h^{2} + 3^{2} = 5^{2}

Area of triangle =

= × 6 × 4

= 12 cm^{2}

Volume of prism = Ah

= 12 cm^{2}× 8 cm

= 96 cm^{3}

**How to find the volume of a rectangular and a triangular prism?**

Step 1: Find the area of the base.

Step 2: Multiply the area of the base times the height.

**How to find the volume of any prism, right or oblique using a general formula?**

The following video shows how to solve a word problem involving the volume of prisms.

**Example:**

Find the volume and capacity of a swimming pool which is made up of a rectangular and trapezoidal prism.

**Use the given net to determine the surface area and volume of a triangular prism**

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