Question
(a) Find the following side lengths for the net.
(b) Use the net to find the surface area of the prism.
(b) Use the net to find the surface area of the prism.
Ask by Stephens Sanders. in the United States
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The surface area of the prism is 332 yd².
Solution
To solve the problem, we need to find the side lengths for the net and then use those lengths to calculate the surface area of the prism.
Part (a): Finding the Side Lengths for the Net
The given dimensions are:
Assuming these dimensions represent the lengths of the edges of a rectangular prism, we can identify the lengths of the sides of the net.
For a rectangular prism, the net consists of:
- 2 rectangles for the top and bottom (length
and width ) - 2 rectangles for the front and back (length
and height ) - 2 rectangles for the left and right sides (width
and height )
Part (b): Finding the Surface Area of the Prism
The surface area
Where:
-
is the length, -
is the width, -
is the height.
Substituting the values into the formula:
Now, let’s calculate the individual products:
Now, summing these products:
Finally, multiplying by 2 to find the total surface area:
Thus, the surface area of the prism is:
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Simplify this solution The Deep Dive
To find the side lengths for the net, let’s first identify the dimensions based on the given measurements. Each side length corresponds to the edges that make up the rectangular faces of the prism. Thus, you would have:
- Length of one rectangle:
- Width of another rectangle:
- Height of one rectangle:
- Base width of the largest rectangle:
Now that we have these dimensions, we can proceed to calculate the surface area of the prism.
To calculate the surface area, you generally add the areas of all the faces. Assuming this is a rectangular prism, the formula is:
Substituting the respective values, if
Calculating:
Adding these:
Now multiplying by 2:
So, the surface area of the prism is
