Surface area of triangular prism base 12 height 8 sides 10 length 6 Step by Step

Step by step

The question

Question: find the surface area of a triangular prism with triangle base 12, height 8 and sides 10, and length 6.

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 12 and height 8.

One triangle is half of base times height: ½ × 12 × 8.

triangle = 12 × 12 × 8

12 times 8 is 96.

triangle = 12 × 96

Half of 96 means 96 divided by 2.

That is 48.

962 = 48

So one triangle is 48 square units.

triangle = 48

The back is the same.

Two triangles: 2 times 48 is 96.

2 triangles = 2 × 48 = 96

3 The three rectangles

The bottom rectangle is 12 by 6.

This one is 10 by 6.

And this one is 10 by 6.

Unroll the three rectangles side by side.

They make one long rectangle: 12 + 10 + 10 wide and 6 long.

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

rectangles = (12 + 10 + 10) × 6

12 plus 10 plus 10 is 32.

rectangles = 32 × 6

32 times 6 is 192.

So the rectangles are 192 square units.

rectangles = 192

4 Add all the faces

Add the triangles and the rectangles: 96 + 192.

S = 96 + 192

96 plus 192 is 288.

So the surface area is 288 square units.

S = 288

Let's look back.

First: count the faces.

Then: the two triangles.

Then: the three rectangles.

Last: add all the faces.

Answer