Answer:
Option 3 is the correct answer
Explanation:
The surface area of a prism is the area of the full net.
The area of the full net is the sum of the areas of each part
For the given net, there are three rectangles, and two triangles.
The area for rectangles and triangles are given by the following formulas:
It is important to recognize that due to the fact that the 3-D shape is a prism, the two triangles are congruent, and have exactly the same dimensions and area.
Looking at the options:
Option 1 has three products added together. This would be the base time height of each of the three rectangles. It does not include the area for either of the triangles.
Option 2 does have an extra term in front with 3 numbers multiplied together. It most closely resembles 2 times the product of the base and height of the triangle, but recall the area for a triangle is one-half of the base times height (this may make more sense when looking at option 3). This over-calculates the area of the triangle, and then doubles that over-calculated area (to match the second triangle)
Option 3 has an extra term in front with the number 2 times a parenthesis with 3 terms. These three terms represent the "one-half" from the formula for the area of a triangle, and the base and height of the triangle. The 2 in front of the parentheses represents that there are two of those triangles, both with that area. This correctly calculates the area of the net, and thus, the surface area of the triangular prism.
Option 4 has an extra term in front, similar to option 3 which calculates the area of one triangle correctly, but fails to account for the area of the second triangle.
Option 3 is the correct answer.