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The first recorded use of areas was in ancient Babylon, where they used it to measure the amount of land that was owned by different populations for taxation purposes. Later in 287 BC, the great mathematician Archimedes from Greece discovered the area and the perimeter of the circle and the relationship between spheres. Archimedes, no doubt, wasn’t the first to realize the fact. However, he was, as far as we know, the first to prove it formally. He also gave the earliest proofs for the volume of the sphere and surface area.
Definition of Area
In geometry, the area can be defined as the space occupied by the surface of an object or any flat shape. The area of an object is the number of unit squares that cover the surface of a closed object. The area is measured in square units such as square feet, square centimeters, square inches, etc.
The origin of the word is from ‘area’ in Latin, which translates to a vacant piece of level ground. This further led to a derivation of the area as a particular amount of space contained within a set of boundaries.
To determine the size of the carpet to be bought, we often find the area of the room floor.
To cover the floor with tiles, to cover the wall with paint or wallpaper or to build a swimming pool are other examples, where the area is computed.
In reality, not every plane surface can be clearly classified as a rectangle, square or a triangle. For finding the area of a composite figure that contains more than one shape, we will find the sum of the area of all the shapes forming the composite figure.
The area of the outside surface of a three-dimensional shape or a solid is called Surface Area of that surface. For example, a rectangular prism has 6 rectangular bases and lateral faces. Thus, the total surface area is equal to the sum of the areas of all 6 rectangles.
Area Formulas
In general, we can say that the area of shapes can be defined as the quantity of paint required to cover the surface with a single coat. These are the following ways to calculate the area based on the number of sides that exist in the shape, as illustrated below in fig.
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What are 3D Shapes?
The three-dimensional shapes, also known as solid shapes, are those which have three dimensions such as length, breadth and thickness. The two different measures which are used to define the three-dimensional shapes are surface area and volume. In general, the 3D shapes are obtained from the rotation of two-dimensional shapes. Thus, the surface area of any two-dimensional shapes should be a 2D shape. If we want to calculate the surface area of any solid shape, we can easily calculate it from the area of 2D shapes.
Area of 3D Shapes Formula
According to the International System of Units (SI), the standard unit of area is the square meter (written as m2) and it is also the area of a square whose sides are one meter long. For example, a definite shape with an area of three square meters would have the same area as three such squares. The surface area of any solid object is a measure of the total area which the surface of the object occupies.
For 3D/ solid shapes like cuboid, cube, cylinder, sphere and cone, the area is updated to the concept of the surface area of the shapes. The formulas for 3D shapes are given in the table below:
Area Formula for Different Shapes
|
Shape |
Area |
Terms |
|
π × r2 |
r = radius of the circle |
|
|
½ × b × h |
b = base h = height |
|
|
a2 |
a = length of side |
|
|
l × w |
l = length w = width |
|
|
b × h |
b = base h = vertical height |
|
|
½(a + b) × h |
a & b are length of parallel sides h = height |
|
|
πab |
a = ½ minor axis b = ½ major axis |
Formulas for 3D Shapes
|
Shape |
Surface Area |
Terms |
|
Cube |
6a2 |
a = length of the edge |
|
Rectangular prism |
2(wl + hl + hw) |
l = length w h = height |
|
Cylinder |
2πr(r + h) |
r = radius of the circular base h = height of the cylinder |
|
Cone |
πr(r + l) |
r = radius of the circular base l = slant height |
|
Sphere |
4πr2 |
r = radius of the sphere |
|
Hemisphere |
3πr2 |
r = radius of the hemisphere |
Know More about Area
The area is defined as a two-dimensional space that is taken up by an object. The concept of the area has a lot of real-life applications. For example; the area is used in farming, building, plotting lands, science and so much more like painting the walls of your room or buying new furniture for the house.
The area can be determined with basic calculations and understanding. The number of square units inside a figure is used to find out the area for a square or rectangle. Sometimes, in the cases of polygons, one can find out the area by multiplying the length by the width.
A=s2 where s is the length of the sides of the square.
A=LW, where L and W are the lengths of the rectangle’s sides (length and width).
A=12bh, where b and h are the base and height.
A=bh, where b is the length of the base and h is the height.
A=πr2, where r is the radius