Net of a triangular prism sides 9, 12, 15, length 6

Step by step

The question

Question: draw the net of a triangular prism, sides 9, 12, 15, length 6, and find its surface area.

The surface area is the area of all the outside faces together.

A net shows every face flat.

1 Unfold it

Flat: three rectangles in a row, and a triangle at each end.

2 Area of each face

The two triangles: half × 9 × 12 is 54.

The 9 by 6 rectangle: 9 × 6 is 54.

The 12 by 6 rectangle: 12 × 6 is 72.

The 15 by 6 rectangle: 15 × 6 is 90.

Careful!

Count every face in the net.

There are two triangles, one at each end.

3 Add them all

We add all 5 faces: 324.

4 Check

Let's check another way.

The three rectangles make one long strip: 36 by 6, that is 216.

Plus the two triangles, 108.

Together 324.

So the answer is right!

Let's look back.

First: unfold it.

Then: area of each face.

Then: add them all.

Last: check.