Surface area of triangular prism sides 3, 4, 5 length 10 Step by Step

Step by step

The question

Question: find the surface area of a triangular prism with triangle sides 3, 4 and 5, and length 10.

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?

3 squared plus 4 squared is 9 plus 16, which is 25.

That is 5 squared.

So yes: the triangle has a right angle.

So its two short sides are its base and height: 4 and 3.

One triangle is half of base times height: ½ × 4 × 3.

triangle = 12 × 4 × 3

4 times 3 is 12.

triangle = 12 × 12

Half of 12 means 12 divided by 2.

That is 6.

122 = 6

So one triangle is 6 square units.

triangle = 6

The back is the same.

Two triangles: 2 times 6 is 12.

2 triangles = 2 × 6 = 12

3 The three rectangles

The bottom rectangle is 4 by 10.

This one is 5 by 10.

And this one is 3 by 10.

Unroll the three rectangles side by side.

They make one long rectangle: 4 + 5 + 3 wide and 10 long.

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

rectangles = (4 + 5 + 3) × 10

4 plus 5 plus 3 is 12.

rectangles = 12 × 10

12 times 10 is 120.

So the rectangles are 120 square units.

rectangles = 120

4 Add all the faces

Add the triangles and the rectangles: 12 + 120.

S = 12 + 120

12 plus 120 is 132.

So the surface area is 132 square units.

S = 132

Let's look back.

First: count the faces.

Then: the two triangles.

Then: the three rectangles.

Last: add all the faces.

Answer