The base of a prism is a triangle with a base of 9 inches and a height of 5 inches. Determine the volume if its length is 18 inches.

Question

UpStudy AI · Accepted Answer

To find the volume of a prism, we can use the formula:

$$
V = B \cdot h
$$

where $$ V $$ is the volume, $$ B $$ is the area of the base, and $$ h $$ is the height (or length) of the prism.

### Step 1: Calculate the area of the triangular base

The area $$ A $$ of a triangle can be calculated using the formula:

$$
A = \frac{1}{2} \cdot b \cdot h
$$

where $$ b $$ is the base of the triangle and $$ h $$ is the height of the triangle.

Given:
- Base of the triangle $$ b = 9 $$ inches
- Height of the triangle $$ h = 5 $$ inches

Substituting the values into the area formula:

$$
A = \frac{1}{2} \cdot 9 \cdot 5
$$

### Step 2: Calculate the area

Now, let's calculate the area:

$$
A = \frac{1}{2} \cdot 9 \cdot 5 = \frac{45}{2} = 22.5 \text{ square inches}
$$

### Step 3: Calculate the volume of the prism

Now that we have the area of the base, we can calculate the volume of the prism. The length of the prism is given as $$ 18 $$ inches.

Using the volume formula:

$$
V = A \cdot l
$$

where $$ l $$ is the length of the prism.

Substituting the values:

$$
V = 22.5 \cdot 18
$$

### Step 4: Calculate the volume

Now, let's calculate the volume:

$$
V = 22.5 \cdot 18 = 405 \text{ cubic inches}
$$

### Final Answer

The volume of the prism is $$ 405 $$ cubic inches.
The volume of the prism is 405 cubic inches.

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