Question
M7|L13 Decomposing Bases for AreaSign out
What is the volume of this prism?
Start by finding the area of the base of the prism. Solve on paper, and then enter your answer on Zearn. You can use the Zearn calculator to help with your calculations.
3D shape with pentagonal base composed of a rectangle with side lengths 4 cm by 6 cm, and a triangle atop the 6 cm length of the rectangle. The triangle is labeled with height 4 cm, and a side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
cm
2
? cm ? cm
3
What is the volume of this prism?
Start by finding the area of the base of the prism. Solve on paper, and then enter your answer on Zearn. You can use the Zearn calculator to help with your calculations.
3D shape with pentagonal base composed of a rectangle with side lengths 4 cm by 6 cm, and a triangle atop the 6 cm length of the rectangle. The triangle is labeled with height 4 cm, and a side length of 3 cm connects the two bases.
Area of the base, B Height of the prism, h Volume, V = B · h
cm
2
? cm ? cm
3
Answers
Answered by
GPT-4o mini
To find the volume of the prism, we need to start by calculating the area of the base.
### Step 1: Find the area of the pentagonal base.
The base consists of a rectangle and a triangle on top of it.
1. **Area of the Rectangle**:
\[
\text{Area of Rectangle} = \text{length} \times \text{width} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2
\]
2. **Area of the Triangle**:
The base of the triangle is 6 cm (the same length as the rectangle), and its height is 4 cm.
\[
\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \, \text{cm} \times 4 \, \text{cm} = 12 \, \text{cm}^2
\]
3. **Total Area of the Base**:
Combine the area of the rectangle and the triangle:
\[
\text{Area of Base (B)} = \text{Area of Rectangle} + \text{Area of Triangle} = 24 \, \text{cm}^2 + 12 \, \text{cm}^2 = 36 \, \text{cm}^2
\]
### Step 2: Find the height of the prism.
The height of the prism is given as ??? cm. It appears to be missing, but assuming it's provided separately, let’s denote the height as \( h \, \text{cm} \).
### Step 3: Calculate the volume of the prism.
Using the formula for the volume of the prism:
\[
V = B \cdot h
\]
where:
- \( B = 36 \, \text{cm}^2 \) (area of the base)
- \( h \) is the height of the prism
Plugging in the values:
\[
V = 36 \, \text{cm}^2 \cdot h \, \text{cm}
\]
### Conclusion
Now, substitute the actual height to get the volume. If \( h \) is provided, calculate \( V \) and enter your answer on Zearn as directed.
For example, if \( h = 5 \, \text{cm} \):
\[
V = 36 \, \text{cm}^2 \cdot 5 \, \text{cm} = 180 \, \text{cm}^3
\]
Make sure to replace \( h \) with the actual height given in your problem for the final calculation.
### Step 1: Find the area of the pentagonal base.
The base consists of a rectangle and a triangle on top of it.
1. **Area of the Rectangle**:
\[
\text{Area of Rectangle} = \text{length} \times \text{width} = 6 \, \text{cm} \times 4 \, \text{cm} = 24 \, \text{cm}^2
\]
2. **Area of the Triangle**:
The base of the triangle is 6 cm (the same length as the rectangle), and its height is 4 cm.
\[
\text{Area of Triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 6 \, \text{cm} \times 4 \, \text{cm} = 12 \, \text{cm}^2
\]
3. **Total Area of the Base**:
Combine the area of the rectangle and the triangle:
\[
\text{Area of Base (B)} = \text{Area of Rectangle} + \text{Area of Triangle} = 24 \, \text{cm}^2 + 12 \, \text{cm}^2 = 36 \, \text{cm}^2
\]
### Step 2: Find the height of the prism.
The height of the prism is given as ??? cm. It appears to be missing, but assuming it's provided separately, let’s denote the height as \( h \, \text{cm} \).
### Step 3: Calculate the volume of the prism.
Using the formula for the volume of the prism:
\[
V = B \cdot h
\]
where:
- \( B = 36 \, \text{cm}^2 \) (area of the base)
- \( h \) is the height of the prism
Plugging in the values:
\[
V = 36 \, \text{cm}^2 \cdot h \, \text{cm}
\]
### Conclusion
Now, substitute the actual height to get the volume. If \( h \) is provided, calculate \( V \) and enter your answer on Zearn as directed.
For example, if \( h = 5 \, \text{cm} \):
\[
V = 36 \, \text{cm}^2 \cdot 5 \, \text{cm} = 180 \, \text{cm}^3
\]
Make sure to replace \( h \) with the actual height given in your problem for the final calculation.