Difference Between Area and Surface Area

Area vs Surface Area

Geometry is a study of shapes. It is broadly classified into two types: plane geometry and solid geometry. Plane geometry deals with two-dimensional figures like square, circle, rectangle, triangle, and many more whereas Solid geometry deals with the study of three- dimensional shapes like cube, cuboid, cylinder, cone, sphere, and many more.

The study of this shape is needed to find lengths, widths, area, surface area, volume, perimeter, and many more terms. Students always get confused between the terms area and surface area. They seem to be similar but they are different concepts. The area is a two-dimensional measurement while surface area is three-dimensional measurement In this article let us discuss the area definition, surface area definition and the difference between area and surface area in detail.

Area Definition

Area definition states that -

The area is the measurement of the space occupied by any two-dimensional geometric shapes. The area of any shape depends upon its dimensions. Different shapes have different areas. For instance, the area of the square differs from the area of the rectangle. The area of a shape is calculated in square units (sq units). As the area is measured for a two-dimensional object it has two dimensions length and width.

Suppose if you want to paint the rectangular wall of your house, you need to know the area of the wall to calculate the quantity of the paint required to paint the wall and the cost of painting.

If two figures have a similar shape it is not necessary that they have equal area unless and until their dimensions are equal. Suppose two squares have sides s and s1, so the areas of the two square will be equal if, s = s1

The formula for Area is a product of length and width.

Surface Area Definition

Surface area definition states that -

The surface area is the area calculated for the three- dimensional object. As the three-dimensional object is made up of 2D faces, surface area is the sum of the areas of all the faces of the figure. Cubes, cuboids, cones, cylinders are some of the three-dimensional objects. Therefore to find the surface area of such 3D objects we have to add the area of all its faces. We can use the basic area formula to calculate its faces as they are simple 2D figures,

For example a cube has six faces. Therefore, its surface area will be the sum of the areas of all the six faces. Since all the sides of a cube are squares, we can express the surface area of a cube as 6 x (Area of a square)

Basically, the surface area can be classified as: 

  • Curved Surface Area (CSA).

The curved surface area of an object is the area of all the curved surfaces in an object. For a right circular cylinder The surface joining the two bases of a right circular cylinder is called its curved surface.

  • Lateral Surface Area (LSA) 

The lateral surface of an object is the area of all the faces of the object, excluding the area of its base and top. For a cube, the lateral surface area would be the area of four sides. 

  • Total Surface Area (TSA) 

Total surface area is the area of all the faces including the bases. For a right circular cylinder, the sum of the lateral surface area or curved surface area and the base areas of both the circles will give the total surface area of the right circular cylinder. 

The area is the measure of a 2-dimensional object, for instance we have to paint a side square wall of a hall. A house is a 3d object but we are only interested in the area of the wall. The surface area is the 2-dimensional measure of the outside of something. For instance by measuring the surface area of your hall we can determine the amount of paint needed to paint all the walls. 

So let us understand the difference between area and surface area in detail.

Key Differences Between Area and Surface Area

Now let us study the relation between area vs surface area.

The differences between area and surface area are given as :

Area vs Surface Area

Area

Surface Area

The area is the measurement of the space occupied by any two-dimensional geometric shapes.

The surface area is the sum of areas of all the faces of the three-dimensional figure.

Plane 2D figures represent the area. Example: circles, rectangles, and triangles.

Solid 3D figures represent the surface area. Examples: cylinder, prisms, pyramids, and cones.

When we have to calculate area all we have to do is concentrate on the area of one figure.

In the surface area, when we have to calculate surface area, we have to work out on the area of all the faces.


Example: The formula of area for the rectangle is – length x width.

Example: The formula to calculate the surface area for a cuboid is – SA = 2lw+2lh+2hw.


Formulas for Area Related to 2D Shapes

Name of Geometric Shapes

Area Formula

Variables

Rectangle

Area = l × w

l =  length

w  = width

Square

Area  = a2

a = sides of the square

Triangle

Area = ½ x b x h

b = base

h = height

Trapezoid

Area = 1/2 (a + b)h

a =base 1

b = base 2

h = vertical height

Parallelogram

Area  = b × h

a = side

b=base

h=vertical height


Rhombus

Area = a x h

a = side of rhombus

h = height

Circle

Area = πr2

r = radius of the circle

= 22/7 or 3.1416

Semicircle

Area = ½ πr2


r = radius of the circle


Formulas for Lateral/ Curved Surface Area and Total Surface Area Related to 3d Shapes(Solid Shapes)

S.No

Name 

Abbreviations used

Lateral /curved Surface Area

Total Surface Area

1.

Cuboid

H = height, 

l = length  b=breadth

2h(l+b)

6l2

2.

Cube

a = length of the sides

4a2

6a2

3.

Right Prism

..

Perimeter of Base × Height

Lateral Surface Area + 2(Area of One End)

4.

Right Circular Cylinder

r= radius

h=height

2 (π × r × h)

2πr (r + h)

5.

Right pyramid

..

½ (Perimeter of Base × Slant Height)

Lateral Surface Area + Area of the Base

6.

Right Circular Cone

r = radius

l = length

πrl

πr (l + r)

7.

Sphere

r = radius

4πr2

4πr2

8. 

Hemisphere

r = radius

2πr2

3πr2


Solved Examples

Find the total surface area of a cylindrical tin of radius 17 cm and height 4 cm.

Solution: 

Given that: r = 17cm and h = 4cm

We have total surface area formula of a cylinder as (TSA) = 2πr (h + r) sq.units

Therefore TSA = 2 x 22/7 x 17(17 + 4)

                           = 2 x 22/7 x 17 x 21

   = 2464cm2

Therefore total surface area of a cylindrical tin is 2464cm2

FAQ (Frequently Asked Questions)

 What is the Difference Between Area and Volume?

Answer: The area refers to the region covered by the object. And volume refers to the quantity or capacity of the object. An area is a two-dimensional object whereas volume is a three-dimensional object. The area is a plain figure while volume is a solid figure. The area covers the outer space and volume covers the inner capacity. The area is measured in square units and volume is measured in cubic units. 

Generally, the area is calculated for two-dimensional objects, while volume is calculated for three-dimensional objects.

Here is the pictorial representation of area and volume which shows the relation between area and volume.

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