Question
What is the volume of this prism?
Start by finding the area of the base. Show your work on paper, then enter your answer on Zearn.
A prism with a pentagonal base decomposed into a rectangle with dimensions 10 cm by 4 cm, and a triangle with a height of 6 cm and a base along the 10 cm side of the rectangle. The distance between the identical bases is labeled 5 cm.
Area of the base, B Height of the prism, h Volume
V = B · h
cm
2
? cm ? cm
3
Start by finding the area of the base. Show your work on paper, then enter your answer on Zearn.
A prism with a pentagonal base decomposed into a rectangle with dimensions 10 cm by 4 cm, and a triangle with a height of 6 cm and a base along the 10 cm side of the rectangle. The distance between the identical bases is labeled 5 cm.
Area of the base, B Height of the prism, h Volume
V = B · h
cm
2
? cm ? cm
3
Answers
GPT-4o mini
To find the volume of the prism, we first need to calculate the area of the base, which consists of a rectangle and a triangle.
### Step 1: Find the area of the rectangle.
The formula for the area of a rectangle is:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}
\]
Given the dimensions of the rectangle:
- Length = 10 cm
- Width = 4 cm
Calculating the area:
\[
\text{Area}_{\text{rectangle}} = 10 \, \text{cm} \times 4 \, \text{cm} = 40 \, \text{cm}^2
\]
### Step 2: Find the area of the triangle.
The formula for the area of a triangle is:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangle:
- Base = 10 cm (along the side of the rectangle)
- Height = 6 cm
Calculating the area:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 \, \text{cm} \times 6 \, \text{cm} = \frac{1}{2} \times 60 = 30 \, \text{cm}^2
\]
### Step 3: Find the total area of the base.
The total area of the base \( B \) is the sum of the area of the rectangle and the area of the triangle:
\[
B = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 40 \, \text{cm}^2 + 30 \, \text{cm}^2 = 70 \, \text{cm}^2
\]
### Step 4: Find the height of the prism.
The height of the prism \( h \) is given as 5 cm.
### Step 5: Calculate the volume of the prism.
The volume \( V \) of the prism is calculated using the formula:
\[
V = B \times h
\]
Substituting the values we found:
\[
V = 70 \, \text{cm}^2 \times 5 \, \text{cm} = 350 \, \text{cm}^3
\]
### Summary:
- Area of the base, \( B = 70 \, \text{cm}^2 \)
- Height of the prism, \( h = 5 \, \text{cm} \)
- Volume, \( V = 350 \, \text{cm}^3 \)
The final answer to enter is:
- Volume = **350 cm³**.
### Step 1: Find the area of the rectangle.
The formula for the area of a rectangle is:
\[
\text{Area}_{\text{rectangle}} = \text{length} \times \text{width}
\]
Given the dimensions of the rectangle:
- Length = 10 cm
- Width = 4 cm
Calculating the area:
\[
\text{Area}_{\text{rectangle}} = 10 \, \text{cm} \times 4 \, \text{cm} = 40 \, \text{cm}^2
\]
### Step 2: Find the area of the triangle.
The formula for the area of a triangle is:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For the triangle:
- Base = 10 cm (along the side of the rectangle)
- Height = 6 cm
Calculating the area:
\[
\text{Area}_{\text{triangle}} = \frac{1}{2} \times 10 \, \text{cm} \times 6 \, \text{cm} = \frac{1}{2} \times 60 = 30 \, \text{cm}^2
\]
### Step 3: Find the total area of the base.
The total area of the base \( B \) is the sum of the area of the rectangle and the area of the triangle:
\[
B = \text{Area}_{\text{rectangle}} + \text{Area}_{\text{triangle}} = 40 \, \text{cm}^2 + 30 \, \text{cm}^2 = 70 \, \text{cm}^2
\]
### Step 4: Find the height of the prism.
The height of the prism \( h \) is given as 5 cm.
### Step 5: Calculate the volume of the prism.
The volume \( V \) of the prism is calculated using the formula:
\[
V = B \times h
\]
Substituting the values we found:
\[
V = 70 \, \text{cm}^2 \times 5 \, \text{cm} = 350 \, \text{cm}^3
\]
### Summary:
- Area of the base, \( B = 70 \, \text{cm}^2 \)
- Height of the prism, \( h = 5 \, \text{cm} \)
- Volume, \( V = 350 \, \text{cm}^3 \)
The final answer to enter is:
- Volume = **350 cm³**.