# Intermediate Geometry : How to find the volume of a prism

## Example Questions

### Example Question #85 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #86 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #87 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #88 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #89 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #90 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #91 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #92 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #93 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.

### Example Question #94 : Prisms

A triangular prism with an equilateral triangle base is placed on top of a rectangular prism with a square base, as shown by the figure below.

Find the volume of the figure.

Explanation:

In order to find the volume of the figure, we will first need to find the volume of the rectangular and triangular prisms.

Recall how to find the volume for any prism:

First find the volume of the rectangular prism:

Next, find the volume of the triangular prism.

Notice that the length of the rectangular prism is the same as the side of the equilateral triangle that makes up one of the bases of the triangular prism.

Recall how to find the area of an equilateral triangle:

Plug in the given side to find the area of the triangle.

Next, notice that the width of the rectangular prism is also the height of the triangular prism.

Now, find the volume of the triangular prism.

To find the volume of the entire figure, add the individual volumes together.

Make sure to round to  places after the decimal.