Part A
<h3>Answer: Net A</h3>
Reason:
This is something you'll have to draw out on paper (or print it out), then fold up the diagram to represent the 3D prism.
Net A has the middle rectangle as the floor. The other rectangles form the vertical left side and the right slanted side. The triangles form the remaining walls.
Folding up net B will have the triangle ABC oriented in the wrong way, and things won't match up perfectly.
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Part B
<h3>Answers: AB = 3, BC = 5, CD = 8.6</h3>
Reason:
When folded up, side AB goes from the floor to the highest point on the prism. This would be the 3 inches marked.
Side BC is the slanted part, and it is 5 inches in length. Note that AB = 3 and AC = 4, so BC = 5 helps make up a 3-4-5 right triangle (refer to the pythagorean theorem).
Lastly, CD = 8.6 is the length or depth of the prism.
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Part C
<h3>Answer:
115.2 square inches</h3>
Reason:
To find the surface area of the 3D prism, we will find the area of each region on the 2D net. This is because the surface area is the amount of wrapping paper needed to enclose the 3D figure.
Let's find the area of triangle ABC
area = base*height/2 = 4*3/2 = 6
Each triangle has an area of 6 square inches. That gives an area of 2*6 = 12 square inches so far for the triangles combined.
Now let's find the perimeter of either triangle:
AB+BC+AC = 3+4+5 = 12
Multiplying this perimeter with the depth of the prism will determine the lateral surface area
12*8.6 = 103.2
Add this lateral area onto the previously calculated triangle combined area (12 square units) and we get 12+103.2 = 115.2 square inches
