Two-dimensional shapes are defined as plane figures consisting of length and breadth. We come across 2D Shapes in our day-to-day life in the form of circles, triangles, squares, rectangles and pentagons. All the shapes are polygons except circles. Each shape has its different properties based on the sides, length, area, angle etc.

Students learn 2D shapes from an early age in order to solve geometrical problems accurately. You can check NCERT Solutions for Class 9 Maths for a better understanding of 2D shapes. We have provided detailed information on 2D shapes in this article. Read on to find out about its definition, types and examples.

Definition of 2D Shapes

2D shapes are the polygon consisting of plane surface measured with length and width or length and height. It consists of vertices and edges. The angles of 2D shapes are measured in degree.

Download NCERT Solutions for Class 9 Maths Chapter 8 PDF

Types of 2D Shapes

There are different types of 2D shapes such as circle, triangle, rectangle, pentagon, square etc. We can say that all the 2D shapes are polygon except for circles. Polygons have a closed structure with sides whereas, circle consists of a curved shape. Let us discuss the types of 2D shapes in detail.

Circle: It is a 2d shape with a closed structure. All the points in the plane are equidistant from a given point known as the centre. The circle consists of different parts based on positions and properties such as annulus, arc, sector, segment, centre, chord, diameter, radius, secant and tangent. The real-life examples of a circle are rings, bangles, wheels, coins etc. The formula of a circle is mentioned below:

(x-h)² + (y-k)² = r²

Triangle: It is a polygon that consists of three edges and three vertices. It consists of the angle formed between two sides of the triangle. The sum of interior angles is 180 degrees. The triangles are differentiated based on length and measurement of angles. Based on length, there are three types of triangles such as scalene, isosceles and equilateral. And based on the measurement of angles, there are three types of triangles i.e., acute, right and obtuse. The formula of a triangle is as follows:

Area = 1/2 × Base × Height

Square: It is a two-dimensional shape consisting of four sides, vertices and angles. There are four internal angles each measuring 90 degrees. The opposite sides of the square are parallel to each other. The diagonals of a square are equal in length, bisect each other, and are perpendicular to each other. The area and perimeter of a square can be calculated by using the formula given below:

Area of a Square =  = a²

Perimeter of a Square = 4a

Rectangle: It is a two-dimensional shape consisting of four sides, vertices and angles. The opposite sides of a rectangle are equal in length and parallel to each other. Also, each of the four internal angles of a rectangle measures 90°. The diagonals of a rectangle bisect each other and are of the same length. The two diagonals of a rectangle bisect each other at different angles one obtuse angle and the other an acute angle. The area and perimeter of a rectangle can be calculated using the formula mentioned below:

Area of a Rectangle = Length (a) × Breadth (b)

Perimeter of a Rectangle = 2 (Length + Breadth) = 2 (a + b)

Pentagon: It is a five-sided two-dimensional polygon. It consists of five angles and sides. The pentagon consists of line segments connected to each other and these line segments are called sides. The point between the line segments is called a vertex. Based on sides, angles and vertices, there are two types of pentagon as Regular and Irregular Pentagon and Convex and Concave Pentagon. The sum of interior angles in the pentagon is 540 degrees. The area and perimeter of the pentagon are calculated by using a formula such as:

Area of a Pentagon, A = (5/2) ×Side Length ×Apothem square units

Perimeter of a pentagon, P = 5a units

Properties of 2D Shapes

Some of the properties of 2D shapes are given below:

2D Shapes	Properties
Circle	1. Circles having equal radii are said to be congruent. 2. The diameter of a circle is the longest chord of the circle. 3. The perpendicular drawn on any given chord of a circle from the centre of the circle bisects the chord into two equal halves. 4. All chords of a circle equidistant from the centre of the circle are equal in length.
Triangle	1. The sum of all three internal angles of a triangle is 180°, i.e. ∠A + ∠B + ∠C = 180°. 2. The sum of all three external angles of a triangle is 360°, i.e. ∠A’ + ∠B’ + ∠C’ = 360°. 3. The measure of an external angle of a triangle is equal to the sum of the measures of the two internal opposite angles. For example, ∠A’ = ∠B + ∠C. 4. The sum of the lengths of any two sides of a triangle is greater than the length of the third side. For example, AB + BC > CA.
Square	1. A square is a quadrilateral with four equal sides and four equal internal angles. 2. It is a rhombus with four equal angles (each angle equals 90°). 3. A square is a rectangle with its two adjacent sides equal. 4. It is a parallelogram with all four internal angles equal to 90° and adjacent sides equal in length.
Rectangle	1. A rectangle is a quadrilateral with four equal internal angles. 2. Each internal angle of a rectangle measures 90°. 3. As the opposite angles of a rectangle are equal, a rectangle is also a parallelogram. 4. The opposite sides of a rectangle are equal and parallel.
Pentagon	1. The sum of interior angles is 540 degrees. 2. It is a regular pentagon if all the sides and angles are equal. 3. It consists of five sides and angles.

Examples of 2D Shapes

Some of the examples of 2d shapes are given below:

Example 1: If the length and the breadth of a rectangle are 8 cm and 5 cm respectively, find its area and perimeter.

Solution: Length of the rectangle, a = 8 cm
Breadth of the rectangle, b = 5 cm.

Area = Length (a) × Breadth (b) = (8 × 5) cm² = 40 cm².
Perimeter = 2 (Length + Breadth) = 2 (8 + 5) = 2 × 13 = 26 cm.

Example 2: Find the area, perimeter, and length of diagonal of a square of side 6 cm.

Solution: Here, length of each side of the square, a = 6 cm.
Therefore,
Area = a²
= 6²
= 36 cm²
Perimeter = 4a
= 4 × 6
= 24 cm
Diagonal = a√2
= √2 × 6
= 8.485 cm.

Also, check:

Properties of Rhombus	Properties of Parallelogram
Properties of Quadrilaterals	Properties of Triangles
Properties of Square	Properties of Rectangle

FAQs

The frequently asked questions on 2d shapes are given below:

Q1. What is the difference between a Square and a Rectangle?
Ans. A Square has all sides equal and opposite sides parallel, whereas Rectangle has only the opposite sides equal.

Q2. What are the types of 2d shapes?
Ans. The types of 2d shapes are circle, rectangle, square, pentagon, triangle etc.

Q3. What is a formula for the perimeter of a square?
Ans. The formula for the perimeter of a square is equal to 4 times the length of each side of the square.
Perimeter = 4 x length of a side of the square.

Q4. What are the different types of triangles?
Ans. On the basis of the length of the sides, there are three types of triangles – Scalene, Isosceles and Equilateral. And, on the basis of measurement of angles, there are three types of triangles: Acute, Right and Obtuse.

Q5. What are the properties of the rhombus?
Ans. Students can refer to this article to know about the properties of a rhombus.

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