Question

The dimensional formula of area is?

Answer 1

Hint: The best way to get the dimension of any term is through the formula of that term. In this question, we should know the formula of area and the SI units of all the quantities mentioned in the formula, which will help us to get the dimension of the term.

Formula used:
$Area=Length\times Breadth$

Complete step by step solution:
We know that formula of area is:-
$Area=Length\times Breadth$
Where, length and breadth are represented as length, and
SI unit of area is ${{m}^{2}}$.
Hence, the dimensional formula of area is ${{L}^{2}}$, which can also be written as ${{M}^{0}}{{L}^{2}}{{T}^{0}}$.

Additional Information:
Area is the quantity that expresses the extent of a two-dimensional figure or shape or planar lamina, in the plane. Surface area is its analog on the two-dimensional surface of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept).
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre , which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.

Note:
SI unit of a variable plays an important role in getting the dimension of a term. From the SI unit we can know, which quantity is dependent on which dimensional constant. Once the dimensional constant is known, then getting the dimensional formula becomes easy.