Surface area of triangular prism base 6 height 4 sides 5 length 10 Step by Step

Step by step

The question

Question: find the surface area of a triangular prism with triangle base 6, height 4 and sides 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

The triangle has base 6 and height 4.

One triangle is half of base times height: ½ × 6 × 4.

triangle = 12 × 6 × 4

6 times 4 is 24.

triangle = 12 × 24

Half of 24 means 24 divided by 2.

That is 12.

242 = 12

So one triangle is 12 square units.

triangle = 12

The back is the same.

Two triangles: 2 times 12 is 24.

2 triangles = 2 × 12 = 24

3 The three rectangles

The bottom rectangle is 6 by 10.

This one is 5 by 10.

And this one is 5 by 10.

Unroll the three rectangles side by side.

They make one long rectangle: 6 + 5 + 5 wide and 10 long.

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

rectangles = (6 + 5 + 5) × 10

6 plus 5 plus 5 is 16.

rectangles = 16 × 10

16 times 10 is 160.

So the rectangles are 160 square units.

rectangles = 160

4 Add all the faces

Add the triangles and the rectangles: 24 + 160.

S = 24 + 160

24 plus 160 is 184.

So the surface area is 184 square units.

S = 184

Let's look back.

First: count the faces.

Then: the two triangles.

Then: the three rectangles.

Last: add all the faces.

Answer