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.
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