Find the surface area of the rectangular prism.
A drawing of a rectangular prism with length 4 inches, width 2 inches and height 3 inches.
The surface area is
square inches.
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You are drawing a net that shows a rectangular prism with an area of 52 square feet. If two of the rectangles in the net are 4 ft.×3 ft., what is the value of the third measurement you need to know to have an area of 52 square feet?
To start, we know that we have two rectangles that are 4 ft. × 3 ft. each, which means they have an area of 12 square feet each. Together, they have an area of 24 square feet.
We also know that the total area of the rectangular prism is 52 square feet.
To find the third measurement, we need to subtract the area of the two rectangles from the total area:
52 sq. ft. - 24 sq. ft. = 28 sq. ft.
So, we need to find a rectangle with an area of 28 square feet. We can do this by multiplying the length and width of the rectangle:
Length × Width = Area
We know that the two rectangles have a width of 3 ft., so:
Length × 3 ft. = 28 sq. ft.
We can solve for the length by dividing both sides by 3:
Length = 28 sq. ft. / 3 ft.
Length ≈ 9.33 ft.
Therefore, the third measurement we need to know is approximately 9.33 ft.
To find the surface area of a rectangular prism, you need to calculate the areas of all its faces and then add them together.
A rectangular prism has six faces:
1. The top face, which is a rectangle with length equal to the length of the prism (4 inches) and width equal to the width of the prism (2 inches). The area of this face is 4 inches multiplied by 2 inches.
2. The bottom face, which is also a rectangle with the same dimensions as the top face. So, the area of this face is also 4 inches multiplied by 2 inches.
3. The front face, which is a rectangle with length equal to the length of the prism (4 inches) and height equal to the height of the prism (3 inches). The area of this face is 4 inches multiplied by 3 inches.
4. The back face, which is the same as the front face. So, the area of this face is also 4 inches multiplied by 3 inches.
5. The left side face, which is a rectangle with width equal to the width of the prism (2 inches) and height equal to the height of the prism (3 inches). The area of this face is 2 inches multiplied by 3 inches.
6. The right side face, which is the same as the left side face. So, the area of this face is also 2 inches multiplied by 3 inches.
To find the total surface area, add up the areas of all six faces:
Total surface area = (4 inches x 2 inches) + (4 inches x 2 inches) + (4 inches x 3 inches) + (4 inches x 3 inches) + (2 inches x 3 inches) + (2 inches x 3 inches).
Now you can calculate the total surface area by performing the multiplication and addition:
Total surface area = 8 square inches + 8 square inches + 12 square inches + 12 square inches + 6 square inches + 6 square inches.
Adding all these values together, you get:
Total surface area = 52 square inches.
Therefore, the surface area of the rectangular prism is 52 square inches.
Find the surface area of the rectangular prism.
A drawing of a rectangular prism with length 4 inches, width 2 inches and height 3 inches.