 ## 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.