2D Shapes

Geometry starts with understanding the simplest and most essential figures: 2D shapes. These flat shapes, like circles, triangles, and squares, are everywhere around us in art, architecture, design, and even nature. They form the foundation of geometry and are key to developing spatial awareness, logical thinking, and measurement skills.

 

Table of Contents

• Definition
• Names of 2D Shapes
• Circle
• Triangle
• Square
• Rectangle
• Pentagon
• Octagon
• Properties of 2D Shapes
• Difference Between 2D and 3D Shapes
• Solved Examples
• Conclusion
• FAQs on 2D Shapes

 

Definition

2D shapes, or two-dimensional shapes, are flat figures that have length and width but no depth or thickness. These shapes are also called plane shapes because they can be drawn on a flat surface like paper.  

All 2D shapes can be measured by area and perimeter, but they do not have volume. These shapes are the foundation of flat geometry and can be found everywhere in real life, including books, signs, floors, artwork, maps, and more.  

Some of the most commonly studied 2D shapes include the circle, triangle, square, rectangle, pentagon, octagon, and other polygons.  

 

Names of 2D Shapes

The following are common 2D shapes used in geometry:  

• Circle: A round shape with no edges.  

• Triangle: A three-sided polygon.  

• Square: A four-sided shape with equal sides and angles.  

• Rectangle: A four-sided shape with equal opposite sides.  

• Pentagon: A five-sided polygon.  

• Octagon: An eight-sided polygon.  

• Polygon: A general term for any 2D shape with three or more straight sides.  

These 2D shapes are grouped based on their number of sides, vertices, and angles.  Let's learn about each in more detail;

 

Circle

What is a Circle?  

A circle is a two-dimensional (2D) closed shape. Every point on its boundary is the same distance from a fixed central point, called the center. The constant distance from the center to any point on the circle is known as the radius. 

A circle does not have sides, angles, or corners like polygons. It is perfectly round and curved, with no edges.

 

Parts of a Circle:  

• Center - The central point from which all points on the boundary are equally distant.  

• Radius (r) - The distance from the center to any point on the circle. All radii in a circle are equal.  

• Diameter (d) - A straight line that goes through the center and connects two points on the boundary. It is twice the radius.  

• (d = 2 × r)  

• Circumference (C) - The total length around the boundary of the circle.  

• Chord - A line segment that connects two points on the boundary, not necessarily through the center.  

• Arc - A part or segment of the circumference.  

• Sector - A portion of the circle enclosed by two radii and an arc.  

• Segment - A part of the circle divided by a chord.  

 

Mathematical Formulas of a Circle:  

• Circumference = 2 × π × r

• Area = π × r²

• Diameter = 2 × r

Where π (pi) is about 3.14 or 22/7.

 

Properties of a Circle:  

• A circle is a 2D curved shape.

• It has no edges and no corners.

• All radii are equal in length.

• The diameter is always twice the radius.

• The circle is symmetrical and has infinite lines of symmetry.

• The circle is not a polygon because it has no straight sides.

• It has a rotational symmetry of order infinity.

• The longest chord in a circle is its diameter.

• Every circle is similar to every other circle.

The circle is often used in design, architecture, and mechanics due to its perfect symmetry.

 

Triangle 

What is a Triangle?  

A triangle is a 2D closed shape with three straight sides and three angles. It is the simplest polygon formed when three line segments join together.  

 

Parts of a Triangle:  

• Vertices, the three corners (labeled A, B, C).  

• Sides, the three line segments (AB, BC, CA).  

• Angles: The three interior angles formed at each vertex.  

• Base, Any one side can be considered the base.  

• Height (altitude), A perpendicular line drawn from a vertex to the opposite side (base).  

 

Types of Triangles:  

• Based on Sides:  

• Equilateral Triangle: All sides and angles are equal.  

• Isosceles Triangle: Two sides and two angles are equal.  

• Scalene Triangle, All sides and angles are different.  

• Based on Angles:  

• Acute Triangle: All angles are less than 90°.  

• Right Triangle: Has one 90° angle.  

• Obtuse Triangle: Has one angle greater than 90°.  

 

Formulas of a Triangle:  

• Perimeter = a + b + c  

• Area = (1/2) × base × height  

• For Heron’s Formula (when all sides are known):  

• s = (a + b + c)/2  

• Area = √[s(s−a)(s−b)(s−c)]  

 

Properties of a Triangle:  

• Has 3 sides, 3 angles, and 3 vertices.  

• The sum of all interior angles is 180°.  

• Triangles can be classified by their sides or angles.  

• It is the strongest shape used in buildings.  

• There are no parallel sides.  

The triangle is one of the most researched 2D shapes in geometry because of its stability and use in calculations.

 

Square

What is a Square?  

A square is a 2D regular quadrilateral with four equal sides and four right angles (90°). It is a type of rectangle and also a rhombus.  

 

Parts of a Square:  

• Sides, 4 equal-length sides.  

• Angles, 4 right angles.  

• Diagonals, 2 equal-length diagonals that bisect each other at 90°.  

 

Formulas of a Square:  

• Perimeter = 4 × side  

• Area = side²  

• Diagonal = side × √2  

 

Properties of a Square:  

• All sides are equal.  

• All angles are 90°.  

• Diagonals are equal and bisect each other at right angles.  

• Has 2 lines of symmetry diagonally and 4 lines of symmetry total.  

• A special type of rectangle and rhombus.  

The square is one of the most perfect and symmetrical 2D shapes.

 

Rectangle

What is a Rectangle?  

A rectangle is a four-sided figure where opposite sides are equal and all angles are right angles. It belongs to the group of parallelograms.  

 

Parts of a Rectangle:  

• Sides - 2 equal lengths and 2 equal widths.  

• Angles - 4 right angles.  

• Diagonals - 2 equal diagonals.  

 

Formulas of a Rectangle:  

• Perimeter = 2 × (length + width)  

• Area = length × width  

• Diagonal = √(length² + width²)  

 

Properties of a Rectangle:  

• Opposite sides are equal and parallel.  

• All interior angles are 90°.  

• Diagonals are equal and bisect each other.  

• It has 2 lines of symmetry. 

The rectangle is one of the most frequently used 2D shapes in architecture and technology.

 

Pentagon  

What is a Pentagon?  

A pentagon is a shape with 5 sides, 5 angles, and 5 corners. If all sides and angles are equal, it is called a regular pentagon; if not, it’s irregular.  

 

Parts of a Pentagon:  

• Sides - 5 line segments.  

• Angles - 5 interior angles.  

• Vertices - 5 points where sides come together.  

 

Formulas of a Pentagon:  

• Perimeter = 5 × side (for regular pentagon)  

• Area = (1/4) × √(5(5 + 2√5)) × side²  

 

Properties of a Pentagon:  

• It has 5 sides and 5 angles.  

• The sum of interior angles is 540°.  

• Each angle in a regular pentagon measures 108°.  

• Irregular pentagons do not have any parallel sides.  

• It has rotational symmetry of order 5 (regular pentagon).  

The pentagon helps introduce more complex polygons in the study of geometry. 

 

Octagon 

What is an Octagon?  

An octagon is a shape with 8 sides, 8 angles, and 8 corners. A regular octagon has all sides and angles equal.  

 

Parts of an Octagon:  

• Sides - 8 straight lines.  

• Angles - 8 internal angles.  

• Vertices - 8 points.  

 

Formulas of an Octagon:  

• Perimeter = 8 × side  

• Area (regular) = 2 × (1 + √2) × side²  

 

Properties of an Octagon:  

• It has 8 sides and 8 angles.  

• The sum of interior angles is 1080°.  

• Each interior angle in a regular octagon measures 135°.  

• It has 8 lines of symmetry if it is regular.  

Among 2D shapes, the octagon is widely used for attention-grabbing signs and decoration.

 

Properties of 2D Shapes 

• 2D shapes are flat and have only length and width. 

• They sit on a plane surface and have no thickness. 

• They have sides, corners, and angles. 

• The perimeter is the total length around the shape. 

• The area is the space covered inside the shape. 

• There is no volume or depth. 

• Polygons are 2D shapes with straight sides, such as triangles and squares. 

• Regular shapes have equal sides and angles. 

• The sum of angles depends on the number of sides. 

• For example, a triangle has 180 degrees. 

• Some shapes have lines of symmetry, like squares and circles. 

• A circle has no sides or corners; it has a radius and a diameter. 

Understanding the properties of 2D shapes helps us recognize, compare, and use these shapes in everyday life. This knowledge builds a strong foundation in geometry.

 

Difference Between 2D and 3D Shapes

 

Understanding the distinction between 2D shapes and 3D shapes is key in identifying shapes in real-life objects.

 

Solved Examples

Example 1:
Find the area and perimeter of a square with a side of 6 cm.
Solution:
Area = 6 × 6 = 36 cm²
Perimeter = 4 × 6 = 24 cm

 

Example 2:
Calculate the area of a rectangle with length 12 cm and width 5 cm.
Solution:
Area = 12 × 5 = 60 cm²
Perimeter = 2 × (12 + 5) = 34 cm

 

Example 3:
Find the circumference of a circle with a radius of 7 cm.
Solution:
Circumference = 2 × π × r = 2 × 3.14 × 7 = 43.96 cm

 

Example 4:
What is the sum of the interior angles of a pentagon?
Solution:
Sum = (n - 2) × 180 = (5 - 2) × 180 = 3 × 180 = 540°

 

Example 5:
Find the area of a regular octagon with side length of 4 cm.
Solution:
Area = 2 × (1 + √2) × side²
= 2 × (1 + 1.414) × 4²
= 2 × 2.414 × 16 ≈ 77.25 cm²

 

Conclusion

2D shapes are important in mathematics and geometry. They help us understand patterns, measurements, and the world around us. By studying 2D shapes like circles, triangles, squares, rectangles, pentagons, octagons, and other polygons, students develop strong spatial and visual skills. 

Each shape has its own identity, properties, and real-world significance. Knowing how to calculate area and perimeter, along with being able to recognize shapes in everyday life, makes geometry both useful and enjoyable.

 

Related Links

Triangles - Learn about different types of triangles, their properties, classification, and real-world applications with easy-to-follow diagrams and examples.

Types of Polygon - Explore the various types of polygons, their characteristics, angles, and sides, with visual aids to enhance understanding.

 

Frequently Asked Questions on 2D and 3D Shapes

1. What is 2D or 3D?

Answer: 

• 2D shapes (two-dimensional) have only length and width. They are flat and cannot be held. Examples: square, circle, triangle.

• 3D shapes (three-dimensional) have length, width, and height (depth). They have volume and occupy space. Examples: cube, sphere, cone.

 

2. Which are 3D shapes?

Answer: Common 3D shapes include:

• Cube - 6 equal square faces

• Cuboid (Rectangular Prism) - 6 rectangular faces

• Sphere - perfectly round, like a ball

• Cylinder - 2 circular faces and 1 curved surface

• Cone - 1 circular face and a pointed vertex

• Pyramid - a polygon base and triangular faces meeting at a vertex

 

3. How to teach 2D shapes?

Answer: Effective ways to teach 2D shapes:

• Use visual aids like flashcards and colorful cut-outs.

• Introduce shapes by name: Circle, Triangle, Square, etc.

• Let students trace shapes or draw them.

• Compare everyday objects to 2D shapes (e.g., clock = circle, window = rectangle).

• Use games and puzzles to make it interactive.

• Encourage group activities using paper folding or sorting.

 

4. Is a coin a 2D or 3D shape?

Answer: A coin is a 3D shape. Though it appears circular from the top (2D), it has thickness, so it is actually a cylinder, which is a 3D shape.

 

5. Is a diamond a 2D shape?

Answer: 

• Yes, in geometry, a diamond shape (also called a rhombus) is a 2D shape.

• It has four equal sides and opposite equal angles.

• It lies flat and has no depth, so it's two-dimensional.

 

Explore key math concepts like 2D shapes, area, perimeter, and symmetry with Orchids The International School!