Question
David bought a jewelry box. He wants to paint all 5 sides of the jewelry box. How much paint does he need?
Do you need to find the surface area or volume of the prism in order to solve this problem?
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
Surface Area
Volume
Great job!
This jewelry box 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 the base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is
in2.
Great job!
Now, find the area of the long rectangle along the edges of the bases. You can use the calculator to help you solve.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is 24 in2.
The area of the long rectangle is
in2.
Excellent!
What is the surface area of this prism? Solve on paper and enter your answer on Zearn. You can use the calculator to help you solve.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is 24 in2.
The area of the long rectangle is 288 in2.
The surface area of this prism is
in2.
Do you need to find the surface area or volume of the prism in order to solve this problem?
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
Surface Area
Volume
Great job!
This jewelry box 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 the base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is
in2.
Great job!
Now, find the area of the long rectangle along the edges of the bases. You can use the calculator to help you solve.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is 24 in2.
The area of the long rectangle is
in2.
Excellent!
What is the surface area of this prism? Solve on paper and enter your answer on Zearn. You can use the calculator to help you solve.
Right triangular prism. Base of the triangular base measures 6 in, its height measures 8 in and the hypotenuse measures 10 in. The height of the prism measures 12 in.
The area of one base is 24 in2.
The area of the long rectangle is 288 in2.
The surface area of this prism is
in2.
Answers
GPT-4o mini
To find the surface area of the right triangular prism, we first need to summarize what we have:
1. The area of one triangular base is \( 24 \, \text{in}^2 \).
2. The height of the prism is \( 12 \, \text{in} \).
### Step 1: Calculate the Area of the Two Triangular Bases
Since there are two identical triangular bases, the total area of the bases is:
\[
\text{Area of both bases} = 2 \times 24 \, \text{in}^2 = 48 \, \text{in}^2.
\]
### Step 2: Calculate the Area of the Long Rectangular Faces
The long rectangular faces correspond to the edges of the triangular base. The lengths of these edges based on the triangular base are as follows:
- One rectangle has dimensions: Height of the prism (12 in) × Length of the base (6 in).
- One rectangle has dimensions: Height of the prism (12 in) × Length of the height of the triangle (8 in).
- One rectangle has dimensions: Height of the prism (12 in) × Length of the hypotenuse (10 in).
Now, let's calculate the areas of these rectangles:
1. Area of rectangle along the base (6 in):
\[
\text{Area} = 6 \, \text{in} \times 12 \, \text{in} = 72 \, \text{in}^2.
\]
2. Area of rectangle along the height (8 in):
\[
\text{Area} = 8 \, \text{in} \times 12 \, \text{in} = 96 \, \text{in}^2.
\]
3. Area of rectangle along the hypotenuse (10 in):
\[
\text{Area} = 10 \, \text{in} \times 12 \, \text{in} = 120 \, \text{in}^2.
\]
### Step 3: Total Area of Rectangular Faces
Summing these areas:
\[
\text{Total area of rectangles} = 72 \, \text{in}^2 + 96 \, \text{in}^2 + 120 \, \text{in}^2 = 288 \, \text{in}^2.
\]
### Step 4: Compute the Total Surface Area of the Prism
Finally, combine the area of the bases and the area of the rectangles:
\[
\text{Surface Area} = \text{Area of both bases} + \text{Total area of rectangles} = 48 \, \text{in}^2 + 288 \, \text{in}^2 = 336 \, \text{in}^2.
\]
So, the surface area of the prism is:
\[
\text{Surface area of the prism} = 336 \, \text{in}^2.
\]
1. The area of one triangular base is \( 24 \, \text{in}^2 \).
2. The height of the prism is \( 12 \, \text{in} \).
### Step 1: Calculate the Area of the Two Triangular Bases
Since there are two identical triangular bases, the total area of the bases is:
\[
\text{Area of both bases} = 2 \times 24 \, \text{in}^2 = 48 \, \text{in}^2.
\]
### Step 2: Calculate the Area of the Long Rectangular Faces
The long rectangular faces correspond to the edges of the triangular base. The lengths of these edges based on the triangular base are as follows:
- One rectangle has dimensions: Height of the prism (12 in) × Length of the base (6 in).
- One rectangle has dimensions: Height of the prism (12 in) × Length of the height of the triangle (8 in).
- One rectangle has dimensions: Height of the prism (12 in) × Length of the hypotenuse (10 in).
Now, let's calculate the areas of these rectangles:
1. Area of rectangle along the base (6 in):
\[
\text{Area} = 6 \, \text{in} \times 12 \, \text{in} = 72 \, \text{in}^2.
\]
2. Area of rectangle along the height (8 in):
\[
\text{Area} = 8 \, \text{in} \times 12 \, \text{in} = 96 \, \text{in}^2.
\]
3. Area of rectangle along the hypotenuse (10 in):
\[
\text{Area} = 10 \, \text{in} \times 12 \, \text{in} = 120 \, \text{in}^2.
\]
### Step 3: Total Area of Rectangular Faces
Summing these areas:
\[
\text{Total area of rectangles} = 72 \, \text{in}^2 + 96 \, \text{in}^2 + 120 \, \text{in}^2 = 288 \, \text{in}^2.
\]
### Step 4: Compute the Total Surface Area of the Prism
Finally, combine the area of the bases and the area of the rectangles:
\[
\text{Surface Area} = \text{Area of both bases} + \text{Total area of rectangles} = 48 \, \text{in}^2 + 288 \, \text{in}^2 = 336 \, \text{in}^2.
\]
So, the surface area of the prism is:
\[
\text{Surface area of the prism} = 336 \, \text{in}^2.
\]