Area of Shapes

Shapes

In our everyday life, we come across a lot of objects of different shapes and sizes. Some of the shapes are squares, rectangles, circles, cones, rhombus. Area and perimeter give us knowledge that helps in dealing with these different forms of object.

In geometry, a shape is defined as an enclosed figure by the boundaries. The enclosed figure consists of lines, angles, points, and curves. There are basically two types of shapes namely:

  1. 2 Dimensional

  2. 3 Dimensional

Every shape has formulas to determine its area, volume, edges, angles and corners, surface area, perimeter, and so on. The formulas are different for both 2D and 3D shapes. Let us discuss further how area and other formulas are calculated.


What is an Area?

An area is a quantity that expresses the closed area in a plane. It is calculated in 2D shapes. The shapes can be drawn on paper. An example includes circle, square, rectangle, trapezium, rhombus, etc. The area will be defined by the surface captured in an enclosed shape. Areas of different shapes are calculated by applying different shape formulas.


Polygon Shapes: It is a 2D shape formed by straight lines. Its example includes triangles, hexagons, and pentagons. The shape is easily identified by its name.

For example, a triangle will consist of 3 lines, a rectangle will consist of 4 lines.

Any shape that consists of 4 different lines is termed a quadrilateral. The area is the enclosed region within that boundary or perimeter of the shape.


2D Shapes

A 2-dimensional shape or also known as flat shapes. They are drawn on the plane and have length and breadth. It does not consist of thickness. The different methods used for the measurement of the area of 2D shapes are area and perimeter. Examples of 2D shapes are square, rectangle, triangle, circle, etc.


The area of a shape is simply calculated as the amount of paint required to cover that enclosed area. Each shape has a different method to calculate its area and perimeter. Let us discuss the area of 2D shapes in a simple tabular form:


Area of 2D Shapes

Shape

Area

Triangle

½ * base * height

Square

Side2

Rectangle

Length * Breadth

Parallelogram

Base * vertical height

Trapezium

½ * ( a+b )* h

Circle

π * radius2

Elipse

π * ½ minor axis * ½ major axis


3D Shapes

These are shapes that have 3 dimensions namely length, breadth, and thickness. Other measures used here are volume and surface area. 3D shapes are formed by the rotation of 2D shapes.


3D solid shapes include a cube, cuboid, sphere, cylinder, and cone. The area of the shape is upgraded to the concept of the surface area of 3D shapes. Each enclosed shape has its area. As discussed earlier, each shape has a different method to calculate the area. Let us discuss the 3D shapes formulae in a tabular form:


Area of the 3D Shape

Shapes

Surface Area

Cube

6a2

Cuboid

2(Length*breadth + breadth*height + height*length)

Cylinder

2π * radius (radius + height)

Cone

π * radius ( radius + slant height )

Sphere

4π * radius2

Hemisphere

3π * radius2


The area formula list is easier understood in tabular form and hence easy to memorize as well.


3D Shapes Formula - Volume And Surface Area

In practical life, we come across a lot of solids which are simply a combination of basic shapes. Its common example includes tents, capsules, and ice-cream cones. These shapes are similar to the basic shapes that we study. They are the combination of simple basic shapes used in our daily life.

3D shapes are a combination of two or more shapes formed from the fusion of basic shapes. They all come together and form a new shape.

While calculating the surface area and volume of 3D shapes, we need to look at the number of solid shapes that form. For example, a cube is formed when six square shapes are joined adjacent to each other. When measuring the surface area and volume of these shapes, all three dimensions such as length, breadth, and height are taken into account.

When finding the surface area of the cuboid, we add the area of each rectangle constituting the cuboid.

FAQs (Frequently Asked Questions)

Q1. What Real-Life Situations Require us to Use the Area?

Ans: To determine the area of all shapes is quite easy to determine. For a square or rectangle, an area is the number of square units inside a figure. The area is also calculated by multiplying the length and its breadth.


The concept of the area has many practical applications. Some of them are listed below:

  1. If looking to sod the lawn, you would need to know the area of the lawn so that it is easier to purchase the right measurement sod for effective and efficient use. This also reduces the wastage.

  2. If you wish to apply carpet in the living area, you need to calculate the area covered in the living area.

  3. I want to lay tiles on the floor and determine how many tiles will be used in a particular area. 

These all are the real-life experiences that would need the requirement to calculate area. This is done to get a basic idea and to also ensure that materials are purchased and applied without any wastage or loss of material.

Q2. How do we Find the Area and Perimeter of an Irregular Shape?

Ans: An irregular shape is any shape that has sides and angles of any length and size.

The following method is used to determine the perimeter and area of irregular shape:

  1. Perimeter: To calculate the perimeter, all sides are added. Their addition is referred to as the perimeter of the irregular shape. We name irregular shapes based on how many sides they have.

  2. Area: To calculate the area of an irregular shape, simply divide the shape into small regular shapes. This makes the calculation of area more precise and easy to calculate. For any 4 sided or 5 sided figure, bifurcate the shape into small regular triangles and calculate the area of the triangle using heron’s formula.

After calculation, the area of each triangle, add all of them to find the area of irregular triangles.