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Difference Between Area and Surface Area
The main difference between area and surface area is that area is used to describe the space occupied by a two-dimensional shape, whereas, surface area is the area occupied by the outer surface of a three-dimensional shape. Geometry is the branch of math that deals with shapes and solid figures, their area, and surface area and volume. In real life, there are many uses of area and surface area. For example, area is used as a measure to calculate the space occupied by a part of a land or if there is a need to paint a certain part of the wall; surface area is used to calculate the total square units of material needed to cover or wrap a cuboidal box.
|1.||What is Area?|
|2.||What is Surface Area?|
|3.||Difference Between Area and Surface Area|
|6.||FAQs on Difference Between Area and Surface Area|
What is Area?
Area is a term associated with two-dimensional figures and shapes like triangles, squares, and rectangles, and it is measured in square units. It can be imagined as the total space or region occupied by a two-dimensional shape on a flat surface. Different figures have different areas. For example, a square has 4 equal sides and the area of a square is the total number of square units occupied by the square and is calculated with the help of the formula: side × side. The area of a triangle is calculated using the formula: 1/2 × base × height. Similarly, different shapes have different formulas to calculate the area.
What is Surface Area?
Surface area is a term that is associated with three-dimensional figures and shapes. In other words, surface area applies to a polyhedron, where a solid shape has flat faces. A cube is a shape that has all its faces in the shape of a square. Therefore, we can say that the surface area of a cube is the sum of the area covered by all the faces of a cube and it is calculated by the formula: Surface area of a cube = 6a2. The formula used to calculate the total surface area of a cuboid = 2(lw+wh+lh), where 'l' is the length, 'w' is the width, and 'h' is the height of the cuboid. In a three-dimensional shape like a cone, the surface area is given by the sum of the curved surface area and the area of its base, which is a circle. The curved surface area is the area of the curved part in a solid shape, whereas, the lateral surface is the difference between the total surface area and the area of the base and top of the shape. It is to be noted that the curved surface area applies only to shapes that have curved surfaces. Observe the following figure which shows the areas and surface areas of 2D and 3D shapes.
Difference Between Area and Surface Area
The table shown below outlines the important differences between area and surface area.
|Area is associated with a two-dimensional shape.||Surface area is associated with a three-dimensional shape.|
|Area is the space or the region occupied by any flat two-dimensional shape.||Surface area is the area or the space occupied by the lateral surface and the area of all the faces of a three-dimensional shape.|
|A few examples of shapes that have an area are square, rectangle, and triangle.||A few examples of solid shapes that have surface area are cube, cuboid, cone, cylinder.|
|Example: Area of a square of side 's' is s × s or s2.||Example: Surface Area of a cube with side 'a' is 6a2. This is because all the faces of a cube are in the form of a square. A cube has 6 faces, therefore, the surface area is 6a2.|
|The calculation of area involves only two dimensions or values. For example, a rectangle's area is calculated by taking its length and width.||The calculation of surface area involves three dimensions or values. For example, the surface area of a cuboid is calculated by taking its length, width, and height.|
|In real life, the area is used to calculate the space or region to be painted on a wall or to calculate the total space occupied by a flat piece of land.||In real life, the surface area is used to calculate the cost of covering a cuboid-shaped box or to paint the surface of a cubical box.|
Topics Related to Difference Between Area and Surface Area
Check out some interesting articles related to area and surface area.
Example 1: Find the area of the following two-dimensional shapes whose dimensions are given.
a) A triangle with a base of 10 units and a height of 8 units.
b) A rectangle with a length of 7 units and a width of 5 units.
a) Given base = 10 units and height = 8 units.
Area of a triangle = 1/2 × base × height
Therefore, the area of the triangle = 1/2 × 10 × 8
= 40 square units.
b) Given, length = 7 units and width = 5 units
Area of a rectangle = length × width
Therefore, area of the rectangle = 7 × 5
= 35 square units.
Example 2: Find the surface area of the following solid shapes.
a) A cube of side 5 units.
b) A cuboid of length 5 units, width 6 units, and height 7 units.
a) Surface area of a cube = 6a2
Given, side of the cube = 5 units.
Therefore, surface area of the cube = 6 × 52
= 6 × 25
= 150 square units.
b) Total Surface area of a cuboid = 2(lw+wh+lh)
Given length = 5 units, width = 6 units and height = 7 units.
Therefore, total surface area of the cuboid = 2[(5 × 6) + (6 × 7) +(5 × 7)]
= 2 (30 + 42 + 35)
= 214 square units.
Therefore, the total surface area of the cube = 214 square units.
FAQs on Difference Between Area and Surface Area
What is Area?
Area is defined as the space occupied by a two-dimensional shape and it is measured in square units. For example, the area of a square is calculated with the help of the formula: side × side.
What is Surface Area?
As the name suggests, surface area is the area that is occupied by the surfaces or the outside parts of a three-dimensional solid. This includes the area of the lateral surfaces as well as the area of its base and top. Usually, the bases of three-dimensional objects are flat two-dimensional shapes. For example, a cube has 6 faces in the form of a square. Its surface area is calculated by summing up the areas of all six faces which is equal to 6a2.
What is Lateral Surface Area?
Lateral surface area is a term that is associated with three-dimensional shapes only. It is the difference between the surface area of the entire object and the areas of its base and the top portion. For example, the lateral surface area of a cylinder is the difference between the total surface area of a cylinder and the area of all of its circular bases at the top and bottom.
What is the Difference Between Area and Surface Area?
Area is the space or region covered by a two-dimensional shape. Only two dimensions are involved in the calculation of area. Surface area is the measure of the total area of the base and top along with any lateral or outside surfaces of a three-dimensional object. The outer area covered by a cone, cube, cuboid, cylinder is considered as the surface area.
What is the Difference Between Curved Surface Area and Lateral Surface Area?
Curved surface area is the area of any curved surface present in a three-dimensional solid. For example, a cone has a curved surface, as well as a flat surface. Lateral surface area includes the surface area of the entire three-dimensional solid other than the base and the top area. For example, the lateral surface area of a cylinder is the difference between the total surface area of the cylinder and the area of the base and top, which are in a circular shape.