Surface Area of a Triangular Prism

0:00This tent shape is a triangular prism. What is its surface area?

0:05Surface area is the total area of all the faces. A face is one flat surface of the solid.

0:13Its two ends are matching triangles, joined by three rectangles, so it has five faces.

0:20Each triangle has a base of 6 centimetres, a height of 4 centimetres and sloped sides of 5 centimetres. The prism is 10 centimetres long.

0:32The height goes straight up from the base to the top corner, at a right angle to the base.

0:38Unfold the prism into a net: a flat shape that folds up to make the solid.

0:44A triangle's area is base times height divided by 2. So 6 times 4 divided by 2 is 12 square centimetres.

0:54There are two triangles, so 2 times 12 is 24 square centimetres.

1:00The bottom rectangle is 6 by 10, so its area is 60 square centimetres.

1:07A common mistake with the sloped rectangles is to use the 4 centimetre height, and work out 4 times 10. But the height is not one of their edges.

1:17Each sloped rectangle is as wide as the triangle's sloped side, 5 centimetres. So each one is 5 times 10, which is 50 square centimetres.

1:29Add the three rectangles: 60 plus 50 plus 50 is 160 square centimetres.

1:37So the surface area is 24 plus 160, which is 184 square centimetres.

1:45Check by adding all five faces: 12 plus 12 plus 60 plus 50 plus 50 is 184.

1:55To find surface area, add the areas of all the faces. Here it is 184 square centimetres.