The invention of the wheel was the prime step of translating objects into geometric shapes. In the early days, the interpretation of “area” using a formula for geometric shapes evolved from the experiments conducted by Archimedes.
The “area” for any object could be explained as:
The amount of material (such as paper, fabric, tiles) required to cover the surface in a 2dimensional plane.
For a 3dimensional object such as sphere, ball, cube or cuboid, it is referred to as the surface area.
Area = ^{1}⁄_{2}× base × height
Area = ^{1}⁄_{2} × b × h 
Area = length × length
Area = l2

Area = length x breadth
Area = l × b

Area = π × radius × radius
Area = π × r2
(π = 3.14)

Using these formulas, area for different quadrilaterals (a special case of polygons with four sides and angles ≠ 90o) is also calculated.
Application
The concept of area is the foundation of geometry since the early days. Scientists and astronomers took the help of patterns and geometric shapes to understand and establish advanced concepts in science and mathematics. In a modern aspect, the mathematical modeling of objects such as machines, tools, wheels as well as garment designing uses the concept of area and perimeter. It also serves as a basis for integral calculus to understand complex objects such as spheres and ellipses.
Fun facts
