Question
Leo bought a jewelry box. He wants to paint all 6 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 trapezoidal prism labeled 3 in, 10 in, 4 in, 5 in, 6 in.
Surface Area
Volume
You got it!
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 one base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right trapezoidal prism labeled 3 in, 10 in, 4 in, 5 in, 6 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?
Right trapezoidal prism labeled 3 in, 10 in, 4 in, 5 in, 6 in.
Surface Area
Volume
You got it!
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 one base on paper, then record your answer on Zearn. You can use the calculator if you need to.
Right trapezoidal prism labeled 3 in, 10 in, 4 in, 5 in, 6 in.
The area of one base is
in2.
Answers
GPT-4o mini
To find the surface area of the right trapezoidal prism, you need to first calculate the area of one of the trapezoidal bases.
Given the dimensions you've provided for the trapezoidal base:
- The lengths of the two parallel sides (bases) are 10 inches and 6 inches.
- The height (the distance between the two bases) is labeled as 4 inches.
The area \(A\) of a trapezoid can be found using the formula:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where \(b_1\) and \(b_2\) are the lengths of the two parallel sides, and \(h\) is the height.
Substituting the values into the formula:
\[
A = \frac{1}{2} \times (10 + 6) \times 4
\]
\[
A = \frac{1}{2} \times 16 \times 4
\]
\[
A = \frac{1}{2} \times 64
\]
\[
A = 32 \, \text{in}^2
\]
So, the area of one trapezoidal base is **32 in²**.
To find the total surface area of the prism, you will also need to calculate the areas of the three rectangular faces connecting the bases.
1. The area of the two trapezoidal bases (2 x 32) = \(32 \times 2 = 64 \, \text{in}^2\).
2. The area of each rectangular face:
- The rectangular face with height 4 inches and the length of one trapezoidal base (10 inches): \(4 \times 10 = 40 \, \text{in}^2\).
- The rectangular face with height 4 inches and the length of the other trapezoidal base (6 inches): \(4 \times 6 = 24 \, \text{in}^2\).
- The rectangular face that connects the two shorter sides (with height 5 inches and base width which can be calculated using the trapezoidal bases length):
The length of this face is equal to the difference of the two bases, which is (10-6)=4 inches.
So, this rectangle area: \(5 \times 4 = 20 \, \text{in}^2\).
Adding these areas together gives you the total surface area:
\[
\text{Surface Area} = \text{Area of both bases} + \text{Area of rectangles}
\]
\[
\text{Surface Area} = 64 + 40 + 24 + 20 = 148 \, \text{in}^2
\]
Therefore, Leo will need paint for **148 in²** of surface area.
Given the dimensions you've provided for the trapezoidal base:
- The lengths of the two parallel sides (bases) are 10 inches and 6 inches.
- The height (the distance between the two bases) is labeled as 4 inches.
The area \(A\) of a trapezoid can be found using the formula:
\[
A = \frac{1}{2} \times (b_1 + b_2) \times h
\]
where \(b_1\) and \(b_2\) are the lengths of the two parallel sides, and \(h\) is the height.
Substituting the values into the formula:
\[
A = \frac{1}{2} \times (10 + 6) \times 4
\]
\[
A = \frac{1}{2} \times 16 \times 4
\]
\[
A = \frac{1}{2} \times 64
\]
\[
A = 32 \, \text{in}^2
\]
So, the area of one trapezoidal base is **32 in²**.
To find the total surface area of the prism, you will also need to calculate the areas of the three rectangular faces connecting the bases.
1. The area of the two trapezoidal bases (2 x 32) = \(32 \times 2 = 64 \, \text{in}^2\).
2. The area of each rectangular face:
- The rectangular face with height 4 inches and the length of one trapezoidal base (10 inches): \(4 \times 10 = 40 \, \text{in}^2\).
- The rectangular face with height 4 inches and the length of the other trapezoidal base (6 inches): \(4 \times 6 = 24 \, \text{in}^2\).
- The rectangular face that connects the two shorter sides (with height 5 inches and base width which can be calculated using the trapezoidal bases length):
The length of this face is equal to the difference of the two bases, which is (10-6)=4 inches.
So, this rectangle area: \(5 \times 4 = 20 \, \text{in}^2\).
Adding these areas together gives you the total surface area:
\[
\text{Surface Area} = \text{Area of both bases} + \text{Area of rectangles}
\]
\[
\text{Surface Area} = 64 + 40 + 24 + 20 = 148 \, \text{in}^2
\]
Therefore, Leo will need paint for **148 in²** of surface area.