Triangular Prism

Triangular Prism

Triangular Prism

A prism having triangular bases is called a triangular prism. A triangular prism has three rectangular faces (lateral surfaces) and two triangular faces (bases) as shown in the figure below.
Triangular Prism and Net of Triangular Prism


Lateral surface area of triangular prism (LSA)

Let a, b and c be the three sides of the triangular base, and h be the height of the prism. Lateral surface area of triangular prism is the area of three rectangular faces (R1, R2 and R3) of the prism as shown in the net of the triangular prism given in the figure below.
Lateral surface area of triangular prism

Lateral surface area (LSA) = area of R1 + R2 + R3
                                              = ah + bh + ch
                                              = (a + b + c)h
                                              = perimeter of triangular base × height
                                              = Ph

Lateral surface area (LSA) = Ph

Total surface area of triangular prism (TSA)

Total surface area of triangular prism is the sum of the lateral surface area and the areas of two triangular bases.
Total surface area (TSA) = LSA + 2 × area of triangular base
                                           = Ph + 2A

Total surface area (TSA) = Ph + 2A

Volume of triangular prism (V)

Volume of triangular prism(V) = Area of triangular base × height of the prism
                                                = A × h

Volume of triangular prism (V) = Ah

Workout Examples

Example 1: Find the lateral surface area, total surface area and volume of the given triangular prism.
Example 1: Triangular prism

Solution: Here, base of prism is right angled triangle,
                              AB = 6cm
                              BC = 8cm                         
AC

                  Perimeter of base (P) = 6 + 8 + 10 =24cm
                    Area of triangular base (A) = ½ AB × BC = ½ × 6 × 8 = 24cm2
                    Height of prism (h) = 20cm

                  Lateral surface area (LSA) = P × h
                                                                  = 24cm × 20cm
                                                                  = 480cm2

                     Total surface area (TSA) = LSA + 2A
                                                                = 480 + 2 × 24
                                                                = 480 + 48
                                                                = 528cm2

                     Volume (V) = A × h
                                         = 24cm2 × 20cm
                                         = 480cm3


Example 2: Find the lateral surface area, total surface area and volume of the given triangular prism.
Example 2: Triangular prism

Solution: Here, base of prism is equilateral triangle of length (a) = 6cm,

                  Perimeter of base (P) = 6 + 6 + 6 =18cm   
Area of equilateral triangle

                    Height of prism (h) = 15cm

                  Lateral surface area (LSA) = P × h
                                                                  = 18cm × 15cm
                                                                  = 270cm2

                     Toral surface area (TSA) = LSA + 2A
                                                                = 270 + 2 × 15.58
                                                                = 270 + 31.16
                                                                = 301.16cm2

                     Volume (V) = A × h
                                         = 15.58cm2 × 15cm
                                         = 233.7cm3


Example 3: Find the lateral surface area, total surface area and volume of the given triangular prism.
Example 3: Triangular prism

Solution: Here, three sides of base triangle are,
                                a = 13cm
                                b = 14cm
                                c = 15cm
                  Perimeter of base (P) = 13 + 14 + 15 =42cm
                     Semi-perimeter (s) = 42/2 = 21cm
               
Area of triangular base

                     Height of prism (h) = 20cm

                  Lateral surface area (LSA) = P × h
                                                                  = 42cm × 20cm
                                                                  = 840cm2

                     Toral surface area (TSA) = LSA + 2A
                                                                = 840 + 2 × 84
                                                                = 840 + 168
                                                                = 1008cm2

                     Volume (V) = A × h
                                         = 84cm2 × 20cm
                                         = 1680cm3


You can comment your questions or problems regarding the area and volume of triangular prisms here.

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