Net of a triangular prism sides 5, 12, 13, length 8

Step by step

The question

Question: draw the net of a triangular prism, sides 5, 12, 13, length 8, 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 × 5 × 12 is 30.

The 5 by 8 rectangle: 5 × 8 is 40.

The 12 by 8 rectangle: 12 × 8 is 96.

The 13 by 8 rectangle: 13 × 8 is 104.

Careful!

Count every face in the net.

There are two triangles, one at each end.

3 Add them all

We add all 5 faces: 300.

4 Check

Let's check another way.

The three rectangles make one long strip: 30 by 8, that is 240.

Plus the two triangles, 60.

Together 300.

So the answer is right!

Let's look back.

First: unfold it.

Then: area of each face.

Then: add them all.

Last: check.