Question
Find the surface area of this rectangular prism.
To find the surface area of a prism, you can add the area of the bases and the area of the long rectangle along the edges of the bases. Start by finding the area of one of the rectangular bases, the highlighted face at the bottom of the prism.
Rectangular prism with the base measuring 4 units by 3 units and the height of the prism measuring 6 units. Bottom base of prism is highlighted.
Area of one base =
square units
Nice!
Now you need to find the area of the long rectangle that’s along the edges of the bases. Press play to unfold the prism to see the long rectangle that’s along the edges of the bases. What is the area of this long rectangle? You can multiply its length by its width. That's the same as multiplying the perimeter of the base by the height of the prism.
Area of one base = 12 square units
Area of the long rectangle =
square units
To find the surface area of a prism, you can add the area of the bases and the area of the long rectangle along the edges of the bases. Start by finding the area of one of the rectangular bases, the highlighted face at the bottom of the prism.
Rectangular prism with the base measuring 4 units by 3 units and the height of the prism measuring 6 units. Bottom base of prism is highlighted.
Area of one base =
square units
Nice!
Now you need to find the area of the long rectangle that’s along the edges of the bases. Press play to unfold the prism to see the long rectangle that’s along the edges of the bases. What is the area of this long rectangle? You can multiply its length by its width. That's the same as multiplying the perimeter of the base by the height of the prism.
Area of one base = 12 square units
Area of the long rectangle =
square units
Answers
GPT-4o mini
To find the surface area of the rectangular prism, we need to calculate the area of the two bases and the area of the four lateral rectangular faces.
1. **Area of one base**:
The base is a rectangle with dimensions 4 units by 3 units.
\[
\text{Area of one base} = \text{length} \times \text{width} = 4 \times 3 = 12 \text{ square units}
\]
Since there are two identical bases, the total area of both bases is:
\[
\text{Total area of both bases} = 2 \times 12 = 24 \text{ square units}
\]
2. **Area of the long rectangle (lateral surface area)**:
The lateral surface area can also be calculated by finding the perimeter of the base and multiplying it by the height of the prism.
First, calculate the perimeter of the base:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (4 + 3) = 2 \times 7 = 14 \text{ units}
\]
Now, multiply the perimeter by the height of the prism (which is 6 units):
\[
\text{Area of the long rectangle} = \text{Perimeter} \times \text{height} = 14 \times 6 = 84 \text{ square units}
\]
3. **Total surface area**:
Now, we can find the total surface area of the prism by adding the area of the two bases and the area of the lateral faces:
\[
\text{Total Surface Area} = \text{Area of both bases} + \text{Area of long rectangle} = 24 + 84 = 108 \text{ square units}
\]
So, to summarize:
- Area of one base = 12 square units
- Area of the long rectangle = 84 square units
- Total Surface Area = 108 square units
Final answer:
- Area of one base = **12 square units**
- Area of the long rectangle = **84 square units**
1. **Area of one base**:
The base is a rectangle with dimensions 4 units by 3 units.
\[
\text{Area of one base} = \text{length} \times \text{width} = 4 \times 3 = 12 \text{ square units}
\]
Since there are two identical bases, the total area of both bases is:
\[
\text{Total area of both bases} = 2 \times 12 = 24 \text{ square units}
\]
2. **Area of the long rectangle (lateral surface area)**:
The lateral surface area can also be calculated by finding the perimeter of the base and multiplying it by the height of the prism.
First, calculate the perimeter of the base:
\[
\text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (4 + 3) = 2 \times 7 = 14 \text{ units}
\]
Now, multiply the perimeter by the height of the prism (which is 6 units):
\[
\text{Area of the long rectangle} = \text{Perimeter} \times \text{height} = 14 \times 6 = 84 \text{ square units}
\]
3. **Total surface area**:
Now, we can find the total surface area of the prism by adding the area of the two bases and the area of the lateral faces:
\[
\text{Total Surface Area} = \text{Area of both bases} + \text{Area of long rectangle} = 24 + 84 = 108 \text{ square units}
\]
So, to summarize:
- Area of one base = 12 square units
- Area of the long rectangle = 84 square units
- Total Surface Area = 108 square units
Final answer:
- Area of one base = **12 square units**
- Area of the long rectangle = **84 square units**