The figure shows the net of a rectangular prism. Which choice is the surface area, in square units, of the prism?
For a rectangular-prism net, first identify the three edge lengths by finding the common height of the side strip and the two different widths that repeat. Then use surface area as “three pairs of matching faces”: compute the areas , , and , double each, and add.
Hints
Identify matching faces
In a net of a rectangular prism, opposite faces are congruent. Look for rectangles with the same dimensions.
Use the repeated measurements
All four side faces share the same height. Use the labeled value on the vertical edges to get that dimension.
Compute using three edge lengths
Once you have the three side lengths of the prism, use for surface area.
Desmos Guide
Enter the surface area expression
In Desmos, enter the expression:
Evaluate the result
Read the value Desmos gives for the expression. That value is the surface area in square units.
Step-by-step Explanation
Read the prism’s dimensions from the net
In the strip of four side faces, each rectangle has height 8.
Two of the rectangles have width 5, and the other two have width 3. That means the base of the prism is a rectangle, and the third dimension (height) is 8.
Find the areas of each pair of congruent faces
A rectangular prism with dimensions 8, 5, and 3 has:
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Two faces with total area
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Two faces with total area
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Two faces with total area
Add to get total surface area
Total surface area .
So the correct choice is 158.