Surface area of triangular prism sides 5, 12, 13 length 4 Step by Step

Step by step

The question

Question: find the surface area of a triangular prism with triangle sides 5, 12 and 13, and length 4.

1 Count the faces

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

This prism has 5 faces: 2 triangles and 3 rectangles.

2 The two triangles

Is there a right angle?

5 squared plus 12 squared is 25 plus 144, which is 169.

That is 13 squared.

So yes: the triangle has a right angle.

So its two short sides are its base and height: 12 and 5.

One triangle is half of base times height: ½ × 12 × 5.

triangle = 12 × 12 × 5

12 times 5 is 60.

triangle = 12 × 60

Half of 60 means 60 divided by 2.

That is 30.

602 = 30

So one triangle is 30 square units.

triangle = 30

The back is the same.

Two triangles: 2 times 30 is 60.

2 triangles = 2 × 30 = 60

3 The three rectangles

The bottom rectangle is 12 by 4.

This one is 13 by 4.

And this one is 5 by 4.

Unroll the three rectangles side by side.

They make one long rectangle: 12 + 13 + 5 wide and 4 long.

So the rectangles are around the triangle, times the length.

rectangles = (12 + 13 + 5) × 4

12 plus 13 plus 5 is 30.

rectangles = 30 × 4

30 times 4 is 120.

So the rectangles are 120 square units.

rectangles = 120

4 Add all the faces

Add the triangles and the rectangles: 60 + 120.

S = 60 + 120

60 plus 120 is 180.

So the surface area is 180 square units.

S = 180

Let's look back.

First: count the faces.

Then: the two triangles.

Then: the three rectangles.

Last: add all the faces.

Answer