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Surface Area of a Triangular Prism

A triangular prism has five faces – there are two congruent triangles (the two ends) and three rectangles. Its cross-section is a triangle.

The surface area of a triangular prism is the sum of the area of these five faces.

So surface area  =  (2 x area of congruent triangles) + (area of bottom face) + (area of left face) + (area of side face).

Let us look at a triangular prism on the left below.

‘Opening up’ this figure will produce a net. A net is a flat diagram that contains the faces of a solid shape. The faces are arranged so that the diagram could be folded to form that solid (in this case, a triangular prism). Drawing the net of a prism can help with calculating the surface area of that particular prism.

surface area of triangular prism_1

So surface area of a triangular prism  =  (2 x 1/2x b x h)  +  (lb + lh + bh)

=  (2 x 1/2x 9 x 12) + (10 x 9)  +  (12 x 10)  +  (15 x 10)

=  108 + 90 + 120 + 150

=  468 cm2

 

surface area of triangular prism_2Example 1 : For the triangular prism shown here, draw a net diagram and then calculate the surface area.

 

 

Let’s first do a net diagram of this triangular prism (shown below) –

surface area of triangular prism_3

Surface area  =  (2 x area of congruent triangles) + (area of bottom face) + (area of left face) + (area of side face)

=  (2 x 1/2x 12 x 5)  +  (10 x 5)  +  (12 x 5)  +  (13 x 10)

=  60 + 50 + 60 + 130

=  300 cm2

 

surface area of triangular prism_4Example 2 : Calculate the surface area of the triangular prism shown here.

 

 

Notice that the triangular faces are isosceles triangles. Doing a net diagram gives us the figure below.

surface area of triangular prism_5

Surface area  =  (2 x area of congruent triangles) + (area of bottom face) + (area of left face) + (area of side face)

=  (2 x 1/2x 12 x 10)  +  (13 x 24)  +  (10 x 24)  +  (13 x 24)

=  120 + 312 + 240 + 312

=  984 cm2

 

surface area of triangular prism_6Example 3 : Find the surface area of the triangular prism here.

Note that the two faces of the triangular prism are isosceles triangles. Also notice that we do not have the height of the triangular faces.

We can find it using Pythagoras Theorem.

surface area of triangular prism_7h  =  sqrt{12.5^2~-~10^2}

=  sqrt{156.25~-~100}

=  sqrt{56.25}

=  7.5 cm

Surface area  =  (2 x area of congruent triangles) + (area of bottom face) + (area of left face) + (area of side face)

=  (2 x 1/2x 20 x 7.5)  +  (12.5 x 16)  +  (20 x 16)  +  (12.5 x 16)

=  150 + 200 + 320 + 200

=  870 cm2