To find the surface area of the rectangular prism, we need to find the area of each of the 6 rectangles in the net and then sum them up.
Let's label the dimensions of the rectangular prism:
Length: L
Width: W
Height: H
There are 2 rectangles with dimensions L x W (top and bottom), 2 rectangles with dimensions L x H (front and back), and 2 rectangles with dimensions W x H (sides).
The surfaces areas of the rectangles are:
- Top and bottom: 2(L x W)
- Front and back: 2(L x H)
- Sides: 2(W x H)
Adding these up:
Surface Area = 2(L x W) + 2(L x H) + 2(W x H)
Surface Area = 2LW + 2LH + 2WH
Therefore, the surface area of the rectangular prism is 2LW + 2LH + 2WH.
Use the image to answer the question.
An illustration shows a two-dimensional net of a rectangular prism composed of 6 rectangles.
The net of a rectangular prism is shown. What is the surface area of the rectangular prism?
3 answers
Wrong
I apologize for the error in my previous response.
Let's label the dimensions of the rectangular prism:
Length: L = 6 cm
Width: W = 4 cm
Height: H = 3 cm
To find the surface area of the rectangular prism, we need to calculate the area of each face and then sum them up.
The area of the top and bottom faces (each with dimensions L x W) is:
2(L x W) = 2(6 cm x 4 cm) = 2(24 cm²) = 48 cm²
The area of the front and back faces (each with dimensions L x H) is:
2(L x H) = 2(6 cm x 3 cm) = 2(18 cm²) = 36 cm²
The area of the side faces (each with dimensions W x H) is:
2(W x H) = 2(4 cm x 3 cm) = 2(12 cm²) = 24 cm²
Now, sum up the areas of all faces to find the total surface area:
Surface Area = 48 cm² + 36 cm² + 24 cm²
Surface Area = 108 cm²
Therefore, the surface area of the rectangular prism is 108 square centimeters.
Let's label the dimensions of the rectangular prism:
Length: L = 6 cm
Width: W = 4 cm
Height: H = 3 cm
To find the surface area of the rectangular prism, we need to calculate the area of each face and then sum them up.
The area of the top and bottom faces (each with dimensions L x W) is:
2(L x W) = 2(6 cm x 4 cm) = 2(24 cm²) = 48 cm²
The area of the front and back faces (each with dimensions L x H) is:
2(L x H) = 2(6 cm x 3 cm) = 2(18 cm²) = 36 cm²
The area of the side faces (each with dimensions W x H) is:
2(W x H) = 2(4 cm x 3 cm) = 2(12 cm²) = 24 cm²
Now, sum up the areas of all faces to find the total surface area:
Surface Area = 48 cm² + 36 cm² + 24 cm²
Surface Area = 108 cm²
Therefore, the surface area of the rectangular prism is 108 square centimeters.