# Surface Area of Prism

Here we will discuss Surface Area of Prism

Prism is named according to the number of edges in the base.
If the common edge of every pair of adjacent lateral faces of prism is perpendicular to the base then it is called right prism.
A prism which is not a right prism is called an Oblique prism.

Properties of Prism

1) The base and top are parallel and congruent.
2) Each face, other than base and top, is a parallelogram. Such face is called a Lateral face.
3) The base has one edge common with every lateral face. The top has one edge common with every lateral face.
4) A common edge of two adjacent side faces is called the height of the prism.

Surface Area of Prism (triangular) :

It consists of two parts : 1) Lateral surface area which is the sum of areas of all lateral faces and 2) The area of base and the top.
Lateral faces of right prism is rectangular.
Area of rectangle = length x width = l x w
Base is triangular so either use 1) Area = ½ x base x height or if the height is not given then use Heron’s formula.
 Area of faces = Lateral area = Perimeter (P) x Height (h) = ph Total surface area = 2 x Area of triangle + ph
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Some solved examples on Surface Area of Prism

1) The base of a triangular prism is ΔABC, where AB = 3 cm, BC = 4 cm and ∠B = 90. If the height of the prism is 10 cm. Find 1) Lateral surface area .
2) Total surface area.
Solution :

As ∠B = 90, so by Pythagorean theorem in ΔABC,
C 2 = a2 + b2
= 32 + 42
= 9 + 16
C2 = 25
C = AC = 5 cm.
Perimeter of Δ ABC = AB + BC + AC = 3 + 4 + 5 = 12 cm
∴ Area of Δ ABC = ½ x 3 x 4 = 6 cm2
Lateral surface area = ph = 12 x 10 = 120 cm2
Total surface area = 2 x area of triangle + ph
⇒ = 2 x 6 + 120
⇒ = 12 +120
∴ Total surface area = 132 cm2.
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2) The base of a triangular prism is an equilateral triangle of side 6 cm. Its height is 8 cm. Find 1) Lateral surface area 2) Total surface area of the prism.
Solution :

Perimeter of ΔABC = p = 3 x 6 = 18 cm
 Area of ΔABC =
Area = √( 9 x 3 x 3 x 3 )
⇒ = 9 √3
Area = 9 x 1.73
Area of ΔABC = 15.57 cm2
Lateral surface area = ph = 18 x 8 = 144 cm2
Total surface area = 2 x area of base + ph
⇒ = 2 x 15.57 + 144
∴ Total surface area = 175.14 cm2

Surface Area :

Surface Area of Cube
Surface Area of Rectangular Prism(Cuboid)
Surface Area of Cylinder
Surface Area of Cone
Surface Area of Sphere and Hemisphere
Surface Area of Prism
Surface Area of Pyramid

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