Question

PLEASE HELP ME OUTT!

Answer 1

156
`in^(2)`

Explanation:

The surface area is, as said by the name, the area of the surface. So, we have to add up all the areas of all the planes. Look at the attachement I edited from the pic you provided.

Planes B and C are both the exact same area, which means the area of one of them is

1/2 * b * h

Now as the area is for both of them, we multiply the above expression by 2 to cancel it out.

2 * 1/2 * b * h

b * h

In this case, our bases and heights for planes B and C are both 6 inches.

So together, planes B and C area

6 * 6 inches square

36 inches square. Remember this.

We will also see that planes A and E have the same area, both being squares as shown from the unfolded version and from the sidelengths of the folded triangular prism.

The area of one plane is b*h, so 2 planes that have the same area would have the area of 2*b*h.

Our base and height for planes A and E are yet again, 6 inches.

So the combined area of the planes are

2*6*6

2*36

72 inches square. Remember this.

Now we have our last plane left, plane D.

This one is a basic plane, just a rectangle.

The area of a rectangle is b * h.

In this case, our area would be

8 * 6

48 inches square. Remember this.

Now for our final answer.

The surface area, using my edited version, would be the following sum:

plane A + plane B + plane C + plane D + plane E

We know that plane B + plane C is equal to 36 inches square.

So, so far we have:

36 + plane A + plane D + plane E

We now that plane A and plane E have a sum that totals to 72 inches square.

Now we have:

36 + 72 + plane D

Substitute the value of plane D and we get:

36 + 72 + 48

36 + 120

156 square inches as our answer

Answer 2

The surface area is the outside part or uppermost layer of something. We want to find the area of all the shapes that make the triangular prism.

The rectangle on top with side lengths of 6 and 8 has an area of 48 in.^2 because 6 x 8 = 48.

The two squares with side lengths of 6 and 6 both have the area of 36 in.^2 because 6 x 6 = 36.

The two triangles have the area of 18 in.^2 because 6 x 6 / 2 = 18.

When you add up the areas of all the shapes you get 48 + 36 + 36 + 18 + 18 = 156 in.^2

Hope this helps :D