Question

In his science class, Boris conducted an experiment in which he used a glass prism to make a rainbow. He now wants to find the surface area of the prism. His teacher gets him a paper model of the prism and spreads it into a flat shape called a net. Boris can see that the net has exactly the same number of faces as the prism. The teacher tells Boris that he can use this net to find the surface area of the prism. Use this image of the net of the prism that Boris’s teacher drew to answer the questions in this activity.

Part A
What is the area of triangle i? Show your calculation.

Part B
Triangles i and ii are congruent (of the same size and shape). What is the total area of triangles i and ii? Show your calculation.

Answer 1

Use the formula for area of the triangle:

• A = 1/2bh, where b- base, h- height or altitude

Part A

The triangle i has:

• b = 4 cm, h = 1.5 cm

The area is:

• A = 1/2*4*1.5 = 3 cm²

Part B

Triangles have same area as they are congruent.

Total area is:

• 3*2 = 6 cm²