A 2D shape (two-dimensional shape) is a flat geometric figure that has only length and width. It has no thickness and can be drawn on a flat surface like paper.
Shapes with three or more straight sides are called polygons, such as triangles, squares, and rectangles.
Properties of 2D Shapes
Understanding the properties of 2D shapes is fundamental in geometry.
- 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.
Types of 2D Shapes
2D shapes are divided into two types based on their sides and interior angles.
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1. Regular 2D Shapes
A regular 2D shape is a two-dimensional figure in which all sides are equal in length and all interior angles are equal in measure. Because of this equality, regular shapes are perfectly symmetrical.
Examples: Square, Equilateral Triangle, Regular Pentagon
2. Irregular 2D Shapes
An irregular 2D shape is a two-dimensional figure in which either the sides, the interior angles, or both are unequal. Because of this variation, irregular shapes do not have complete symmetry.
Examples: Scalene Triangle, Irregular Quadrilaterals
2D Shapes Names
There are many 2D shapes in geometry. Some of them are commonly seen around us. Below is a list of common 2D shapes.
Circle
A circle is a closed two-dimensional (2D) shape formed by a curved line. It has no sides, corners, or edges.
- Every point on the boundary (circumference) is at an equal distance from the centre.
- Some real-life examples of a circle are coins, wheels, and pizzas.
- A circle has important parts such as the radius, diameter, and circumference.
Triangle
A triangle is a two-dimensional polygon with three sides, three vertices, and three angles.
- The sum of its interior angles is always 180 degrees.
- It is one of the simplest and most fundamental shapes in geometry.
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.
- It has a straightforward formula for calculating its area and perimeter:
Area = Length ⨉ readth
Perimeter = 2( Length + Breaths).
Pentagon
A pentagon is a two-dimensional polygon with five sides and five angles.
- The sum of its interior angles is 540 degrees.
- It is a commonly seen geometric shape in architecture and design due to its distinctive five-sided form.
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
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.\
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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.