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.

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 (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.

Solution: Here, base of prism is right angled triangle,

                              AB = 6cm

                              BC = 8cm                         

                ∴  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.

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

                ∴  Perimeter of base (P) = 6 + 6 + 6 =18cm   

                    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.

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

               

                     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.