NETS AND SURFACE AREA

Example 1 :

Find the surface area of the square pyramid given below.

Solution :

Make a net of this square pyramid, and use the net to find the surface area.

Step 1 :

Make a net of the pyramid.

Draw the square base, draw a triangle on each side and label the dimensions.

Step 2 :

Use the net to find the surface area.

There are four triangles with base 16 in. and height 17 in.

The area of the 4 triangles is

= 4 x (1/2) x 16 x 17

= 544 in²

The area of the base is

= 16 x 16

= 256 in²

Hence, the required surface area is

= 544 + 256

= 800 in²

Example 2 :

A sculpture sits on pedestal in the shape of a square prism. The side lengths of a base of the prism are 3 feet. The height of the prism is 4 feet. The museum director wants to cover all but the underside of the pedestal with foil that costs $0.22 per square foot. How much will the foil cost?

Solution :

From the given information, we have the following figure. 

Step 1 :

Use a net to show the faces that will be covered with foil.

Draw the top.

Draw the faces of the prism that are connected to the top.

We don’t need to include the bottom of the pedestal.

Step 2 :

Use a net to show the faces that will be covered with foil.

Use the net to find the area that will be covered with foil.

Area of top = 3 x 3

= 9 ft²

The other four faces are identical.

Area of four faces = 4 x 3 x 4

= 48 ft²

Area to be covered = 9 + 48

= 57 ft²

Step 2 :

Find the cost of the foil.

57 x $0.22 = $12.54

The foil will cost $12.54.

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