Question
Arnav bought a gift. He wants to wrap the gift with wrapping paper. What is the exact amount of wrapping paper he would need to completely cover the gift without any excess?
Do you need to find the surface area or volume of the prism in order to solve this problem?
L-shaped prism labeled 6 in, 10 in, 18 in, 30 in, 6 in, 24 in, 20 in.
Surface Area
Volume
Nice!
This gift is in the shape of a prism. One way you can find the surface area is by adding the area of the 2 bases, and the area of the long rectangle along the edges of the bases. Start by finding the area of one base on paper, then record your answer on Zearn. You can use the calculator if you need to.
L-shaped prism labeled 6 in, 10 in, 18 in, 30 in, 6 in, 24 in, 20 in.
The area of one base is
in2.
Do you need to find the surface area or volume of the prism in order to solve this problem?
L-shaped prism labeled 6 in, 10 in, 18 in, 30 in, 6 in, 24 in, 20 in.
Surface Area
Volume
Nice!
This gift is in the shape of a prism. One way you can find the surface area is by adding the area of the 2 bases, and the area of the long rectangle along the edges of the bases. Start by finding the area of one base on paper, then record your answer on Zearn. You can use the calculator if you need to.
L-shaped prism labeled 6 in, 10 in, 18 in, 30 in, 6 in, 24 in, 20 in.
The area of one base is
in2.
Answers
GPT-4o mini
To find the surface area of an L-shaped prism, we must first determine the area of one base, which is typically composed of two rectangular sections.
Let's break down the dimensions that you have provided and find the area of one base of the L-shaped prism:
1. The L-shape can be viewed as a large rectangle with a smaller rectangle removed from it.
2. The dimensions are given as:
- The first rectangle (the largest part) has a length of 30 inches and a width of 6 inches.
- The smaller rectangle that is "cut out" has a length of 20 inches and a width of 6 inches.
To find the area of one base:
### Step 1: Calculate the area of the larger rectangle:
\[
\text{Area}_{\text{large}} = \text{length} \times \text{width} = 30\, in \times 6\, in = 180\, in^2
\]
### Step 2: Calculate the area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = \text{length} \times \text{width} = 20\, in \times 6\, in = 120\, in^2
\]
### Step 3: Subtract the area of the small rectangle from the area of the large rectangle to find the area of the base:
\[
\text{Area}_{\text{base}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}}
\]
\[
\text{Area}_{\text{base}} = 180\, in^2 - 120\, in^2 = 60\, in^2
\]
So, the area of one base of the L-shaped prism is **60 in²**.
Now, to find the total surface area, you would also need to account for the sides of the prism. Since different dimensions are mentioned (10 in, 18 in, 24 in), you would need to consider those dimensions for the other rectangular faces.
### Surface Area Summary:
- Start with the area of the two bases (2 × 60 in²).
- Add the areas of the lateral faces (rectangles using the dimensions 10 in, 18 in, 24 in, etc.).
Total surface area would involve summing all these areas together.
### Final Note:
To completely answer your question about wrapping the gift without any excess, you need to calculate the total surface area of the prism since that will tell you the exact amount of wrapping paper you need. Volume is not relevant in this context.
Let's break down the dimensions that you have provided and find the area of one base of the L-shaped prism:
1. The L-shape can be viewed as a large rectangle with a smaller rectangle removed from it.
2. The dimensions are given as:
- The first rectangle (the largest part) has a length of 30 inches and a width of 6 inches.
- The smaller rectangle that is "cut out" has a length of 20 inches and a width of 6 inches.
To find the area of one base:
### Step 1: Calculate the area of the larger rectangle:
\[
\text{Area}_{\text{large}} = \text{length} \times \text{width} = 30\, in \times 6\, in = 180\, in^2
\]
### Step 2: Calculate the area of the smaller rectangle:
\[
\text{Area}_{\text{small}} = \text{length} \times \text{width} = 20\, in \times 6\, in = 120\, in^2
\]
### Step 3: Subtract the area of the small rectangle from the area of the large rectangle to find the area of the base:
\[
\text{Area}_{\text{base}} = \text{Area}_{\text{large}} - \text{Area}_{\text{small}}
\]
\[
\text{Area}_{\text{base}} = 180\, in^2 - 120\, in^2 = 60\, in^2
\]
So, the area of one base of the L-shaped prism is **60 in²**.
Now, to find the total surface area, you would also need to account for the sides of the prism. Since different dimensions are mentioned (10 in, 18 in, 24 in), you would need to consider those dimensions for the other rectangular faces.
### Surface Area Summary:
- Start with the area of the two bases (2 × 60 in²).
- Add the areas of the lateral faces (rectangles using the dimensions 10 in, 18 in, 24 in, etc.).
Total surface area would involve summing all these areas together.
### Final Note:
To completely answer your question about wrapping the gift without any excess, you need to calculate the total surface area of the prism since that will tell you the exact amount of wrapping paper you need. Volume is not relevant in this context.