2d shapes

In geometry, 2d shapes and 3d shapes are explained widely to make you understand the different types of objects you come across in real life. These shapes have their own pattern and properties. Depending on many factors, such as angle, sides, length, height, width, area, volume, etc., the shapes can vary. These 2D and 3D shapes have been taught to us since our primary classes. Let us learn various types of two-dimensional shapes here, in this article.

2D Shapes Definition

In maths, 2d shapes can be defined as the plane figures that can be drawn on a flat (or plane) surface or a piece of paper. All the 2d shapes have various parameters such as area and perimeter. Some of the 2d shapes contain sides and corners, whereas some have curved boundaries.

2D Shapes Names

1. Circle
2. Triangle
3. Square
4. Rectangle
5. Pentagon
6. Octagon

The basic types of 2d shapes are a circle, triangle, square, rectangle, pentagon, quadrilateral, hexagon, octagon, etc. Apart from the circle, all the shapes are considered polygons, which have sides. A polygon that has all the sides and angles equal is called a regular polygon. Including the circle, an ellipse is also a non-polygon shape. Both circles and ellipse have a curved shape, whereas the polygons have a closed structure with sides. Now let us discuss some shapes one by one.

Circle

A circle is a closed 2d figure in which the set of all the points in the plane is equidistant from a given point called the “center”. The distance from the center to the outer line of the circle is called a radius. The example of the circle in real life are wheels, pizzas, orbits, etc.

Triangle

A triangle is a three-sided polygon (2d Shape) that has three edges and three vertices. The sum of all the three angles of a triangle is equal to 180°. Pyramids are the best example of a triangle shape.

Square

A square is a four-sided polygon (2d Shape), whose four sides are equal in length and all the angles are equal to 90°. It is considered to be a two-dimensional regular quadrilateral. The diagonals of the square also bisect each other at 90°. A wall or a table where all the sides are equal are examples of square shapes.

Rectangle

A rectangle is a 2d shape that has four sides, where the opposite sides are equal and parallel to each other. All the angles of a rectangle are equal to 90°. A brick, TV, and cardboard, which have length and breadth are examples of the rectangle.

Pentagon

A pentagon is a five-sided polygon (2d Shape), and it can be regular or irregular. In the case of a regular pentagon, each interior angle is equal to 108°, and each exterior angle measures 72°. It has five diagonals. The Pentagon building, which is the headquarters of the US Department of Defense, is a great example of the Pentagon shape.

Octagon

An octagon is an eight-sided polygon which can be either regular or irregular. It is a 2d shape which has eight angles. The sum of all the interior angles of an octagon is 1080°. The stop sign board has an octagon shape, which you can see on the roadside.

2D Shapes Properties

Go through the below to learn all the properties of 2D shapes.

2 D Shapes	It can have up to 2 axes of symmetry
Square	Four equal sides	Four equal angles(90°)	Four axes of symmetry
Rectangle	2 sets of 2 equal sides	Four equal angles(90°)	Two axes of symmetry
Triangle	It can have no, 2 or 3 equal sides	It can have no, 2 or 3 equal angles	Almost infinite axes of symmetry going through the center
Circle	Constant diameter andradius	The total angle of a circle is equal to 360 degrees	It can have up to 5 axes of symmetry
pentagon	5 sides (can be equal or unequal)	5 angles (can be equal or unequal)	It can have up to 6 axes of symmetry
hexagon	6 sides (can be equal or unequal)	6 angles (can be equal or unequal)	It can have up to 8 axes of symmetry
Octagon	8 sides (can be equal or unequal)	8 angles (can be equal or unequal)	It can have a line of symmetry
Parallelogram	2 sets of 2 equal sides	2 sets of 2 equal angles	Usually no axes of symmetry
Rhombus	All sides the same length	2 sets of 2 equal angles	2 lines of symmetry
Trapezium	At least 2 parallel sides	Can have pairs of equalangles	Can have pairs of equal angles

Area and Perimeter of 2D Shapes

The area is the region covered by a 2d shape on a plane. The areas for different shapes are given below:

2d Shape	Area	Perimeter
Circle	Πr2 (R is the radius of the circle)	2πr
Triangle	½ (Base x height)	Sum of three sides
Square	Side2	4(Side)
Rectangle	Length x Breadth	2(Length + Breadth)
Rhombus	½ (Product of diagonals)	4(Side)
Parallelogram	Base x Height	2 (Base + Side)

2d Shapes and 3d Shapes

We know that 2d shapes are flat figures and 3d shapes are solid figures. Below are a few comparisons of these two types of shapes.

2d Shapes	3d Shapes
It is a shape surrounded by three or more straight lines in a plane and sometimes with a closed curve.	If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape.
These shapes have no depth or height.	These are also called solid shapes and unlike 2D they have height or depth.
Area, and perimeter can be found for these shapes.	We can calculate their volume, CSA, LSA, or TSA.
These are shapes containing three dimensions such as depth (or height), breadth, and length.	We can calculate their volume, CSA, LSA or TSA.
Examples: Circle, Triangle, Quadrilaterals, Polygons, etc.	Examples: Cube, Cuboid, Sphere, Cylinder, Cone, etc.

Solved Examples

Q.1: What is the area of a square that has a side length equal to 4 inches?

Solution: Given, the length of the side of the square = 4 inches

Area of square = side² = (4) = 16 in²

Q.2: What is the area of a circle whose radius is 7 cm? (π=22/7)

Solution: Given, the radius of the circle = 7 cm

Area of circle = πr² = (22/7) x 7² = 22 x 7 = 154 sq.cm.

Q.3: Find the perimeter of the rectangle whose length and breadth are 10 cm and 5 cm, respectively. Also, find its area.

Solution: Given, 

Length of rectangle = 10 cm

Breadth of rectangle = 5 cm

Area of rectangle = Length x Breadth = 10 x 5 = 50 cm²

Perimeter of rectangle = 2(Length + Breadth) = 2(10+5) =  2 x 15 = 30 cms