Surface area of prisms

Triangular prisms

We can apply the same strategy to finding the total surface area of all prisms, that is, unfolding the net to identify all individual faces.
When you take slices through a triangular prism parallel to the base you get triangles identical to the base. So the area of each slice is always the same.

Question 3

This solid triangular prism needs all its faces painted.
The area of each triangular face is 3 m².
What is the total area (m²) to be painted?

Solution

In order to paint all the faces of the triangular prism above we need to find the area of the individual faces of the prism.

In this question, the triangular base is an isosceles triangle, therefore two of the rectangles are identical. The faces of the triangular prism are two identical triangles (bases) and three rectangles.

Surface area of each triangular face is 3 m².

Surface area of the two identical rectangles	= 5 × 2.5 × 2
	= 25 m²

Surface area of the third rectangle	= 5 × 3
	= 15 m²

Total surface area	= the sum of all individual areas
	= 2 × 3 + 25 + 15
	= 46 m²

Therefore the total area of the triangular prism to be painted is 4 m².

Question 1

Question 4