## What is Surface Area definition in Maths?

A surface area is an area of surfaces or faces in any object or place. The unit of the surface area is square meters, square feet, square centimeters, etc. as per convenience.

### Types of surface area

There are two types of surface area-

**Total surface area**- The sum of the area of all surfaces or faces in any object is known as its total surface area.

**Lateral surface area (**

**Curved Surface Area)**- Total surface area of the object minus the area of the top & bottom faces is known as the lateral surface area (curved surface area).

### What are the uses of surface area in daily life?

The surface area is mainly used in the field of construction where we want to put the number of tiles on the floor, the coloring of walls, in the carpentry shop, designing, etc.

We use Square, Rectangle, Triangle, Circle, Cube, Cuboid, Cylinder, Sphere, Hemisphere, Cone, etc. shapes in our daily life and find their surface area by formulas.

We also use various combined shapes to find the surface area and these combined shapes we may see in oil tankers, gas tankers (hemisphere+cylinder), etc.

### List of all Surface area formulas

We have various formulas to find the surface area-

*1.) Surface area of square = Side×Side*

2.) Surface area of rectangle = Length×Breadth

3.) Surface area of circle = Ï€r²

4.) Surface area of right triangle = (1/2)×Base×Height

5.) Total Surface area of cube formula = 6a²

2.) Surface area of rectangle = Length×Breadth

3.) Surface area of circle = Ï€r²

4.) Surface area of right triangle = (1/2)×Base×Height

5.) Total Surface area of cube formula = 6a²

6.) Lateral surface area of cube formula = 4a²

7.) Total Surface area of cuboid formula = 2×{lb+bh+hl}

8.) Lateral surface area of cuboid formula = 2×{bh+hl}

9.) Total Surface area of cylinder = 2Ï€r×{r+h}

10.) Curved Surface area of cylinder = 2Ï€rh

11.) Total Surface area of cone = Ï€r×{l+r}

12.) Curved Surface area of cone = Ï€rl

13.) Total Surface area of sphere = 4Ï€r²

14.) Curved Surface area of sphere = 4Ï€r²

15.) Total Surface area of hemisphere formula = 3Ï€r²

16.) Curved Surface area of hemisphere = 2Ï€r²

6.) Lateral surface area of cube formula = 4a²

7.) Total Surface area of cuboid formula = 2×{lb+bh+hl}

8.) Lateral surface area of cuboid formula = 2×{bh+hl}

9.) Total Surface area of cylinder = 2Ï€r×{r+h}

10.) Curved Surface area of cylinder = 2Ï€rh

11.) Total Surface area of cone = Ï€r×{l+r}

12.) Curved Surface area of cone = Ï€rl

13.) Total Surface area of sphere = 4Ï€r²

14.) Curved Surface area of sphere = 4Ï€r²

15.) Total Surface area of hemisphere formula = 3Ï€r²

16.) Curved Surface area of hemisphere = 2Ï€r²

### How to find the surface area of any shape?

To find the surface area of any shape we need dimensions of the shape such as its length, breadth, radius, slant height, height, etc. If we have all dimensions of the shape then we put it into the formula & find their surface area.

Let us understand with some examples:

**Find the total surface area of the cube if its edge is 4 cm.**

Solve:-

Given, Edge of the cube=4cm.

Total Surface of cube = 6a²

= 6×(4)²

= 6×16

= 96 cm²

**Find the surface area of a rectangular prism if its length, width, and height are 5m, 4m, and 3m respectively.**

Solve:

Given, Length of prism=5m, Width of prism=4m, and height of prism=3m

Rectangular prism and cuboid are the same in shape so the formula of total surface area and lateral surface area of rectangular prism and cuboid are the same.

The total surface area of rectangular prism=2×(lb+bh+hl)

=2×[(5×4)+(4×3)+(3×5)]

=2×[20+12+15]

=2×47

=94 sq.m

The lateral surface area of rectangular prism=2×(bh+hl)

=2×[(4×3)+(3×5)]

=2×[12+15]

=2×27

=54 sq.m

**Find the surface area of the prism if its length, breadth, and height are 10cm each.**

Solve:

Given, Edge of the prism=10cm

Square prism and cude are the same in shape if both have equal length, breadth, and height.

Total Surface of square prism = 6a²

= 6×(10)²

= 6×100

= 600 cm²

Lateral Surface of square prism = 4a²

= 4×(10)²

= 4×100

= 400 cm²

**Find the volume and surface area of a cuboidal water tank 3m long, 2m wide, and 2m deep.**

Solve:

Given, Length of tank=3m, Width of tank=2m, Height of tank= 2m

The volume of cuboidal water tank = length×breadth×height

= l×b×h

= 3m×2m×2m

= 12 cubic meter.

The total surface area of the cuboidal water tank=2×(lb+bh+hl)

=2×[(3×2)+(2×2)+(2×3)]

=2×[6+4+6]

=2×16

=32 sq.m