2D-Shapes

Two-dimensional and Three-dimensional shapes are important geometrical figure concepts in mathematics. 2D shapes are flat figures that have only length and width. They lack depth or thickness. 2D shapes are flat while 3D shapes have depth and volume.

In this article, we will discuss about 2D-shapes in detail.

2D Shapes Definition

Two-dimensional (2D) shapes are geometric figures that exist on a flat plane, with only length and width, lacking depth. They are fundamental in geometry and play a crucial role in various mathematical and real-world applications.

Mathematical Representation of 2D Shapes

2D shapes are often represented by their defining characteristics, such as the number of sides, angles, and whether they have equal sides or angles. Formulas for calculating their properties, like area and perimeter, are also used in mathematical representation.

Examples: Common examples of 2D shapes include squares, rectangles, circles, triangles, pentagons, hexagons and octagons.

2D Shapes Names

Listed below are different 2D Shapes with brief descriptions of each of them:

Circle

A circle is a closed curve where all points on its circumference are equidistant from its centre. It has no angles and is characterized by its radius and diameter. A circle is a closed curve with all points on its circumference equidistant from its centre. It is defined by its radius and diameter and infinite symmetrical properties.

Triangle

A triangle is a polygon with three sides and three angles. The sum of its interior angles is always 180 degrees. A triangle is a polygon characterized by three sides and three angles, with the sum of its interior angles always totaling 180 degrees. It is one of the simplest and most versatile 2D shapes.

Square

A square is a quadrilateral with four equal sides and four right angles. Its properties include equal diagonals and symmetry about its center. In simpler words, a square is a four-sided polygon with all sides equal in length and all angles measuring 90 degrees. It exhibits symmetry about its center and is often encountered in both mathematical and real-world contexts.

Rectangle

A rectangle is a quadrilateral with opposite sides equal and all angles at 90 degrees. Its properties include equal diagonals and symmetry about its center. Its properties include equal diagonals and a straightforward formula for calculating its area and perimeter.

Pentagon

A pentagon is a polygon with five sides and five angles, with the sum of its interior angles totaling 540 degrees. A pentagon has five sides and five angles. The sum of its interior angles is 540 degrees. It is notable for its distinctive shape and appearance in architecture and design.

Types of 2D Shapes

When we explore the world of geometry, we observe various types of 2D shapes, each with unique characteristics and properties. Listed below are different types of 2D shapes:

Triangles

Triangles are three-sided polygons characterized by straight sides and angles. They come in different forms such as equilateral (all sides and angles are equal), isosceles (two sides and angles are equal) and scalene (no sides or angles are equal).

Quadrilaterals

These are four-sided polygons. Examples include squares (all sides equal, all angles 90 degrees), rectangles (opposite sides equal, all angles 90 degrees), parallelograms (opposite sides parallel and equal), rhombuses (all sides equal) and trapezoids (one pair of parallel sides).

Circles

Circles have a curved shape with no straight sides or angles. They are defined by a single continuous curve and are characterized by their radius (distance from the center to any point on the circle) and diameter (twice the radius).

Polygons

Polygons are closed shapes with straight sides. They can have any number of sides, from three (triangle) to infinity (circle). Regular polygons have all sides and angles equal, while irregular polygons have sides and/or angles of varying lengths and measures.

2D shapes can be classified as regular or irregular. Below listed are the characteristics of Regular and Irregular 2D Shapes:

• Regular shapes have all sides and angles equal.

• Irregular shapes have varying side lengths and angle measures.

Listed below are tabular differences between Regular and Irregular 2D Shapes:

Parameter	Regular 2D Shapes	Irregular 2D Shapes
Definition	Shapes with equal side lengths and angles	Shapes with varying side lengths and angles
Symmetry	High degree of symmetry	Lacks symmetry
Examples	Square, equilateral triangle, regular pentagon	Rectangle, parallelogram, trapezoid, irregular polygon
Properties	All sides and angles are equal	Sides and/or angles may differ in length and measure

Properties of 2D Shapes

Understanding the properties of 2D shapes is fundamental in geometry. Here are some key properties:

• Sides: 2D shapes are defined by their sides, which are straight lines connecting points. The number of sides varies depending on the shape.

• Angles: Angles are formed where two sides of a shape meet.

• Vertices: Vertices are the points where two sides of a shape meet. The number of vertices is equal to the number of sides.

• Symmetry: Some 2D shapes exhibit symmetry, meaning they can be divided into two identical halves. Examples include squares and circles.

• Diagonals: Diagonals are straight lines connecting non-adjacent vertices in a polygon.

2D Shapes and 3D Shapes

Listed are the tabular differences between 2D Shapes and 3D Shapes

Parameter	2D Shapes	3D Shapes
Definition	Flat shapes with two dimensions (length and width)	Solid shapes with three dimensions (length, width, and height)
Representation	Represented on a plane surface	Represented in space
Properties	Determined by sides and angles	Determined by edges, faces, and vertices
Perimeter/Area	Perimeter encloses the shape, area covers its surface	Surface area encloses the shape, volume fills its space
Examples	Triangle, square, circle, rectangle	Cube, sphere, cylinder, pyramid, cone

Area and Perimeter of 2D Shapes

• Area of 2D Shapes: Area of a 2D shape is the amount of space it occupies in a plane. The formulas for calculating the area vary depending on the type of shape.

• Perimeter of 2D Shapes: Perimeter of a 2D shape is the total length of its boundary. It is calculated by adding the lengths of all its sides.

Thus, Perimeter of 2D Shapes encloses the shape and Area of 2D Shapes covers its surface their formulas are added below:

Formula for Finding Perimeter of 2D Shape

Perimeter of a 2D shape can be calculated using specific formulas based on its dimensions and properties. In simpler terms, the perimeter of a 2D shape is the sum of the lengths of all its sides.

Formula for finding the perimeter of a 2D shape depends on its type:

• For Triangle: P = a + b + c, where a, b and c are the lengths of the sides.

• For Quadrilateral: Perimeter is the sum of the lengths of all four sides.

• For Circle: C = 2πr, where r is the radius.

• For Regular Polygon: P = n⋅s, where n is the number of sides and s is the length of each side.

Formula for Finding Area of 2D Shape

Area of a 2D shape is calculated using specific formulas based on its dimensions and properties. Formula for finding the area of a 2D shape depends on its type:

• For Triangle: A = 1/2×b×h, where b is base of triangle, h is height of triangle.

• For Quadrilateral: A = b×h, where b is base of quadrilateral, h is height of quadrilateral.

• For Circle: C = πr², where r is the radius.

Understanding 2D shapes is fundamental in various fields such as architecture, engineering, art and design. 2D shapes are used to create and understand objects and structures in our surroundings.

From constructing buildings to creating digital graphics, knowledge of 2D shapes is essential for visualizing and designing structures, objects and artistic compositions.

Examples on 2D Shapes

Example 1: Find the perimeter of a rectangle with length 6 cm and width 4 cm.

Solution:

Perimeter = 2 × (Length + Width)

Perimeter = 2 × (6 cm + 4 cm)

= 2 × 10 cm

= 20 cm

Example 2: Calculate the area of a circle with radius 5 cm.

Solution:

Area = π × (Radius)²

= π × (5 cm)²

= π × 25 cm²

≈ 78.54 cm²

Example 3: Find the area of a triangle with base 8 units and height 10 units.

Solution:

Area = 0.5 × Base × Height

= 0.5 × 8 units × 10 units

= 40 square units

Example 4: Calculate the perimeter of an equilateral triangle with side length 12 cm.

Solution:

Perimeter = 3 × Side Length

= 3 × 12 cm

= 36 cm

Example 5: Determine the area of a square with side length 7 meters.

Solution:

Area = Side Length × Side Length

= 7 meters × 7 meters

= 49 square meters

Practice Questions on 2D – Shapes

Q1: Calculate the perimeter of an equilateral triangle with side length 6 cm.

Q2: Calculate the area of a circle with radius 7 cm.

Q3: Find the perimeter of a rectangle with length 5 cm and width 3 cm.

Q4: Find the area of a triangle with base 8 units and height 10 units.

Q5: Find the area of a triangle with base 6 units and height 12 units.

FAQs on 2D – Shapes

What are 2d Shapes?

2D (two-dimensional) shape are defined as a plane figure that are drawn on a flat surfaces. These shapes have only two dimensions – length and width, with no thickness or depth.

What are regular 2D shapes?

2D shapes with all sides equal are called regular shapes. For example, equilateral triangle, square, regular pentagan, etc.

How can we classify 2D shapes based on their angles?

2D shapes can be classified as polygons or non-polygons with polygons further categorized based on the number of sides and angles.

What is the difference between regular and irregular 2D shapes?

Regular 2D shapes have all sides of equal length and all angles of equal measure, while irregular 2D shapes have sides and/or angles of different lengths or measures.

How do we calculate the area of a 2D shape?

Area of a 2D shape depends on its type. For example, the area of a rectangle is found by multiplying its length and width, while the area of a circle is calculated using the formula πr² where r is the radius.

How is a circle defined in geometry?

A circle is a closed curve where all points on its circumference are equidistant from its center.

What distinguishes a square from other 2D shapes?

A square is a quadrilateral with all sides equal in length and all angles measuring 90 degrees.

How is a rectangle different from a square?

Unlike a square, a rectangle has opposite sides equal in length while all angles still measure 90 degrees.

Can 2D shapes be curved?

Yes, some 2D shapes, like circles and ellipses have curved boundaries.

What are some real-world examples of 2D shapes?

Examples include rectangular shape of a phone screen, the circular shape of a CD, the triangular shape of a pizza slice and the hexagonal shape of a bolt head.