**Surface area of prism :**

Prism is basically a 3D shape. Even though we have different formulas to find surface area of different kinds of prisms, the basic idea of finding surface area of a prism is to add the areas of all the faces.

To understand how to find surface area of a prism, let us consider the rectangular prism given below.

Here is the basic idea to find surface area of the above rectangular prism.

**Surface Area = Sum of areas of all six faces**

Let us find the area of each face separately.

**Area of the front face (red colored) = l x h**

**Area of the back face (blue colored) = l x h**

**Area of the left side face (green colored) = w x h**

**Area of the right side face (green colored) = w x h**

**Area of the top portion (purple colored) = l x w**

**Area of the ****base (purple colored) = l x w**

Now,

Surface area = lh + lh + wh + wh + lw + lw

Surface area = 2lh + 2wh + 2lw

**Surface area of = 2( lh + wh + lw )**

This is the formula to find surface area of a rectangular prism.

Note : Rectangular prism is also known as cuboid.

We can apply the above explained basic idea to find surface area of any prism without remembering the formulas.

Let us find surface area of the cube given below.

We know that the shape of each face of a cube is a square.

In the above cube, the side length of each face is "a".

So, area of each face (square) = a x a = a²

Therefore,

surface area of the cube = 6 x area of each face

**Surface area of cube = 6a²**

**Now, let us find surface area of the triangular prism given below. **

In the above triangular prism, there are five faces. The shape of the base and the two slanting faces is rectangle. The shape of two faces on the left side and right side is triangle.

For the given triangular prism,

Area of the base = Lb

Area of the first slanting face = Ls

Area of the other slanting face = Ls

Area of the front face = (1/2)bh

Area of the back face = (1/2)bh

So,

surface area = sum of the area of 5 faces

surface area = Lb + 2Ls +2x(1/2)bh

**Surface area of triangular prism = Lb+2Ls+bh**

**Problem 1 : **

Find the surface area of the cuboid given below.

**Solution : **

**Surface area of cuboid = Sum of areas of all six faces**

In cuboid, each face is a rectangle. So we can use area of rectangle formula to get area of each face.

Area of the front face = 8 x 12 = 96 sq. cm

Area of the back face = 8 x 12 = 96 sq.cm

Area of the left side face = 4 x 8 = 32 sq.cm

Area of the right side face = 4 x 8 = 32 sq.cm

Area of the top portion = 4 x 12 = 48 sq.cm

Area of the base = 4 x 12 = 48 sq. cm

**Surface area of cuboid = Sum of areas of all six faces**

Surface area of cuboid = 96 + 96 + 32 + 32 + 48 + 48

Surface area of cuboid = 96 + 96 + 32 + 32 + 48 + 48

**Surface area of cuboid = 352 sq. cm**

**Alternative method : **

We can use the formula given below to find surface area of cuboid.

**Surface area of cuboid = 2(lh + wh + lw) **

Here, l = 12 cm, w = 4 cm and h = 8 cm.

Surface area of cuboid = 2(12x8 + 4x8 + 12x4)

Surface area of cuboid = 2(96 + 32 + 48)

Surface area of cuboid = 2(176)

**Surface area of cuboid = 352 sq.cm**

Let us look at the next problem on "Surface area of prism"

**Problem 2 : **

Find the surface area of the cube given below.

**Solution : **

We know that the shape of each face of a cube is a square.

In the above cube, the side length of each face is "8".

So, area of each face (square) = 8 x 8 = 64 sq.cm

Therefore,

surface area of the cube = 6 x area of each face

surface area of the cube = 6 x 64

**Surface area of the cube = 384 sq.cm**

Let us look at the next problem on "Surface area of prism"

**Problem 3 : **

Find the surface area of the triangular prism given below.

**Solution :**

In the above triangular prism, there are five faces. The shape of the base, vertical face and slanting face is rectangle. The shape of two faces on the left side and right side is triangle.

For the given triangular prism,

Area of the base = 7 x 4 = 28 sq.cm

Area of the vertical face = 3 x 7 = 21 sq.cm

Area of the slanting face = 5 x 7 = 35 sq. cm

Area of the front face = (1/2) x 4 x 3 = 6 sq.cm

Area of the back face = (1/2) x 4 x 3 = 6 sq.cm

So,

surface area = sum of the area of 5 faces

surface area = 28 + 21 + 35 + 6 + 6

**Surface area of the triangular prism = 96 sq.cm**

Let us look at the next problem on "Surface area of prism"

**Problem 4 : **

Find the surface area of the triangular prism given below.

In the above triangular prism, there are five faces. The shape of the base and the two slanting faces is rectangle. The shape of two faces on the left side and right side is triangle.

For the given triangular prism,

Area of the base = 8 x 12 = 96 sq.cm

Area of the first slanting face = 12 x 5 = 60 sq.cm

Area of the other slanting face = 12 x 5 = 60 sq. cm

Area of the front face = (1/2) x 8 x 3 = 12 sq.cm

Area of the back face = (1/2) x 8 x 3 = 12 sq.cm

So,

surface area = sum of the area of 5 faces

surface area = 96 + 60 + 60 + 12 + 12

**Surface area of the triangular prism = 240 sq.cm**

Let us look at the next problem on "Surface area of prism"

**Problem 5 : **

Find the surface area of the triangular prism given below.

In the above triangular prism, there are five faces. The shape of the base and top portion is triangle. The shape of the faces being as side walls of the prism is rectangle.

For the given triangular prism,

Area of the base = (1/2) x 6 x 4 = 12 sq.cm

Area of the top portion = (1/2) x 6 x 4 = 12 sq.cm

Area of the front face (rectangle) = 6 x 8 = 48 sq.cm

Area of the first back face (rectangle) = 8 x 5 = 40 sq.cm

Area of the other back face (rectangle) = 8 x 3 = 24 sq.cm

So,

surface area = sum of the area of 5 faces

surface area = 12 + 12 + 48 + 40 + 24

**Surface area of the triangular prism = 136 sq.cm**

After having gone through the stuff given above, we hope that the students would have understood "Surface area of prism".

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