Question
Ahmed wants to paint this box. How much paint does Ahmed need to cover all sides of the box?
Do you need to find the surface area or volume of the box in order to solve this problem?

Volume
Surface area
Excellent!
This 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. Find the area of one base on paper, then record your answer on Zearn. You can use the calculator to help you solve.

The area of one base is
24
in2.
Excellent!
Now, find the area of the long rectangle along the edges of the bases. You can use the calculator to help you solve.

The area of one base is 24
in2.
The area of the long rectangle is
192
in2.
Excellent!
Now, find the surface area of the prism to figure out how much paint Ahmed needs. Solve on paper if you'd like, then enter your answer on Zearn.

The area of one base is 24
in2.
The area of the long rectangle is 192
in2.
The surface area of this prism is
in2 so Ahmed will need
216
in2 of paint to cover the box.
Do you need to find the surface area or volume of the box in order to solve this problem?

Volume
Surface area
Excellent!
This 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. Find the area of one base on paper, then record your answer on Zearn. You can use the calculator to help you solve.

The area of one base is
24
in2.
Excellent!
Now, find the area of the long rectangle along the edges of the bases. You can use the calculator to help you solve.

The area of one base is 24
in2.
The area of the long rectangle is
192
in2.
Excellent!
Now, find the surface area of the prism to figure out how much paint Ahmed needs. Solve on paper if you'd like, then enter your answer on Zearn.

The area of one base is 24
in2.
The area of the long rectangle is 192
in2.
The surface area of this prism is
in2 so Ahmed will need
216
in2 of paint to cover the box.
Answers
GPT-4o mini
To find the surface area of the box (which is in the shape of a prism), you need to calculate the total area of all the sides of the box.
You have already found the area of one base to be 24 in². Since there are two bases, the total area of the bases is:
\[
\text{Area of both bases} = 2 \times 24 \, \text{in}^2 = 48 \, \text{in}^2
\]
You've also found the area of the long rectangle (the lateral surface area) to be 192 in².
Now, to find the total surface area of the prism, you add the area of both bases to the area of the long rectangle:
\[
\text{Surface area} = \text{Area of both bases} + \text{Area of the long rectangle}
\]
Substituting the values:
\[
\text{Surface area} = 48 \, \text{in}^2 + 192 \, \text{in}^2 = 240 \, \text{in}^2
\]
Therefore, the surface area of the prism is **240 in²**. So, Ahmed will need **240 in²** of paint to cover the box.
You have already found the area of one base to be 24 in². Since there are two bases, the total area of the bases is:
\[
\text{Area of both bases} = 2 \times 24 \, \text{in}^2 = 48 \, \text{in}^2
\]
You've also found the area of the long rectangle (the lateral surface area) to be 192 in².
Now, to find the total surface area of the prism, you add the area of both bases to the area of the long rectangle:
\[
\text{Surface area} = \text{Area of both bases} + \text{Area of the long rectangle}
\]
Substituting the values:
\[
\text{Surface area} = 48 \, \text{in}^2 + 192 \, \text{in}^2 = 240 \, \text{in}^2
\]
Therefore, the surface area of the prism is **240 in²**. So, Ahmed will need **240 in²** of paint to cover the box.