Question

A prism and two nets are shown below:

Image of a right triangular prism and 2 nets. The triangle bases have base 4, height 3, and diagonal side 5. The length of the prism from the bases is 8.6. Net A has 3 rectangles in a row. The middle one has sides AC and CD. This middle one has triangle ABC on top and identical triangle below. Net B is the same except that the triangle base ABC is on top of the last rectangle which has sides AC and CD. Units are in inches.

Part A: Which is the correct net for the prism? Explain your answer.

Part B: Write the measurements of Sides AB, BC, and CD of the correct net.

Part C: What is the surface area of the prism? Show your work.

Answer 1

Explanation:

a) Imagine folding the net into the shape. In this case, Net A can have both triangles fold up, and both rectangles fold in to make the above shape.

b) Side AB on this net is the height of the triangle, 3 inches.

Side BC is the same as the hypotenuse (diagonal) on the triangle, which . is 5 inches.

Side CD is the same as the length of the shape, which is 8.6 inches.

c) Surface area = area of all sides

Triangle = 1/2 bh

= 2*3

= 6 inches squared

There are two triangles, so that adds to 12 inches squared.

Now all of the rectangles:

Left most = 3*8.6

= 25.8 inches squared

Middle = 4*8.6

= 34.4

Right most = 5*8.6

= 43

Now we can add all of this:

43 + 34.4 + 25.8 + 12

= 115.2 inches squared.

This is the surface area of the prism.