Plane Figure in Math – Definition, Properties, Facts, Examples

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What Are Plane Figures in Geometry?

A plane figure is a flat shape. It does not have depth or thickness. Plane figures only have two dimensions (length and width). Thus, they are also known as 2D figures or two-dimensional shapes.

Some common examples of geometric plane figures are squares, rectangles, circles, triangles, etc.

Plane figures

A plane figure lies all within a single plane. A plane shape can consist of straight line segments, curved lines, or a combination of both. You can easily draw plane figures on a piece of paper. Try drawing the following plane figures on paper!

Plane shapes examples:

Plane figures examples

Plane Figure: Definition

A plane figure is a flat geometric shape with no thickness composed of curves, line segments, or a combination of both.

Plane figure examples: Squares, rectangles, circles, triangles, etc.   

Plane figures

What Are the Properties of Plane Figures?

  • Sides: Sides of plane figures are the line segments that form their boundaries.
  • Vertices: Vertices are the corners points where the sides of a plane figure meet.
  • Angles: Angles are formed where two sides meet.
  • Perimeter and Area: The perimeter of a plane figure is the total length of its boundary, It is the sum of its side-lengths. The area of a closed plane figure is the measure of the space it occupies within its boundary. It is measured in square units.
  • Property of Symmetry: Some plane figures exhibit symmetry; they can be divided into two equal halves that are mirror images of each other.
  • Types: Plane figures can be classified into various types, including triangles, quadrilaterals, polygons, circles, and more.
  • Diagonals: Diagonals are line segments that connect non-adjacent vertices within certain plane figures, like polygons.
  • Regular and Irregular Plane Figures: Plane figures can be regular if all their sides and angles are equal. Plane figures are called irregular if they have varying side lengths and angles.

Plane Figures vs. Solid Figures

Suppose you draw a house on a piece of paper. Can you identify the difference between this house and the one you live in? The basic difference is that the house drawn on the paper is a two-dimensional figure. We can also call it a plane shape. But the house you live in is a three-dimensional figure. We call it a solid shape.

Plane FiguresSolid Figures
A plane shape has two dimensions.A solid shape has three dimensions.
Plane figures are also called plane shapes, flat shapes, or two-dimensional shapes.Solid figures are also called solids, solid shapes, or three-dimensional shapes.
A plane shape has no depth or thickness.A solid shape has depth or thickness.
Plane shape examples include triangles, circles, squares, rectangles, etc.Solid shape examples include pyramid, cone, sphere, cube, cuboid, etc.  
Plane figuresSolids

What Are Open Figures and Closed Figures?

We can classify a plan shape as open or closed.

  • What Are Open Figures?

In open figures, there are holes in the boundary. The starting point and the endpoint of open shapes are different. 

Open shapes
  • What Are Closed Figures?

A closed figure is a geometric figure that has no open ends. The boundary of closed shapes does not have holes. You can say that they have the same starting point and endpoint.

The figure below provides a few examples of closed plane geometrical figures.

Close plane figures

What Are Polygons?

A polygon is a closed plane figure formed by line segments with at least 3 sides. 

The name of a polygon is based on the number of its sides. Usually, a polygon is referred to as a n-gon, where n refers to the number of sides.

Examples of polygons include squares, triangles, rectangles, pentagons, hexagons, octagons, etc.

Examples of polygons

What Are Non-Polygonal Plane Figures?

A non-polygonal plane shape is a plane figure that is not a polygon. A plane figure is not considered a polygon if any of its sides are curved.

Examples of non-polygonal figures include a circle and an ellipse.  

Non-polygonal plane shapes

Common Examples of Plane Figures

SquareA square is a 2D plane shape with 4 equal sides, 4 vertices, and 4 right angles. There are two diagonals which bisect each other at 90 degrees.Square
RectangleA rectangle is a 2D plane shape having 4 sides, 4 vertices, and 4 right angles. The opposite sides of the rectangle are equal and parallel to each other. Diagonals bisect each other.Rectangle
TriangleA triangle is a polygon that has 3 sides. When you add the measures of 3 angles of a triangle, the sum always equals 180 degrees. A triangle can be classified into different types based on its sides and angles.Triangle
CircleA circle is a plane shape with a curved boundary. It is a collection of points that are equidistant from a fixed point, called the center. The fixed distance is called the radius.Circle
PentagonA pentagon is a plane figure; it is a polygon with 5 sides. Pentagon
OctagonAn octagon is a polygon with 8 sides. Octagon

Facts about Plane Figures

  • Plane figures are two-dimensional shapes that lie entirely within a flat plane.
  • A polygon having equal sides and equal angles is called a regular polygon. For example, a square is a regular polygon.
  • Every square is also a rectangle. However, every rectangle isn’t a square.

Conclusion

In this article, we learned about plane figures 

Solved Examples on Plane Figures

Example 1: Which of the following is a polygon?

Ellipse, Circle, Oval, Quadrilateral

Solution: 

A quadrilateral is a polygon having four sides and four vertices. 

A polygon is a closed plane figure composed of line segments with a minimum of 3 sides. Polygons do not have curved edges. 

Ellipse, circle, and oval shape are not polygons. They all have a curved boundary.

Example 2: How can we identify an open plane shape? Give an example.

Solution: 

If an open plane figure has holes in the boundary; its starting point and endpoint are different.  

Here’s an example of an open plane figure:

Open shape example

Example 3: Is the given plane figure a polygon?

An irregular shape

Solution: 

No, the given plane shape is not a polygon.

It is not composed of line segments. 

Its boundary is curved.

Example 4: Is the given figure a closed shape or an open shape?

A plane figure of a pine tree

Solution: 

The given plane figure is a closed shape since it has no open ends. 

Its boundary has no holes.

Practice Problems on Plane Figures

Plane Figure in Math - Definition, Properties, Facts, Examples

Attend this quiz & Test your knowledge.

1

Identify a plane figure.

Sphere
Cylinder
Circle
Pyramid
CorrectIncorrect
Correct answer is: Circle
A sphere, a cylinder, and a pyramid are all solids. A circle is a plane shape.
2

Which shape from among the options is not a plane shape?

Rectangle
Ellipse
Square
Cube
CorrectIncorrect
Correct answer is: Cube
A cube is a 3D shape. It's not a plane shape.
3

What kind of shape is the given figure?

Plane Figure in Math – Definition, Properties, Facts, Examples
Polygonal plane shape
Non-polygonal plane shape
Pentagon
None of the above
CorrectIncorrect
Correct answer is: Non-polygonal plane shape
Since the given figure is a closed flat shape with a curved portion, it is a non-polygonal plane shape.
4

Which of the following plane shapes is not a polygon?

Ellipse
Square
Triangle
Octagon
CorrectIncorrect
Correct answer is: Ellipse
An ellipse has a closed curved boundary. It is not a polygon.
5

Which of the following statements is false?

A 2D shape has no depth.
A plane polygonal shape has vertices and edges.
Every open 2D shape has a well-defined area.
A rhombus is a closed 2d shape.
CorrectIncorrect
Correct answer is: Every open 2D shape has a well-defined area.
Since open 2D shapes don't have a closed boundary, they don't have a well-defined area.

Frequently Asked Question on Plane Figures

The diameter of a circle is a line segment that connects two points located on the boundary of the circle. This line segment passes through the center of the circle.

Yes, we can form a closed plane shape using just one line segment and a curve. The shape formed will be a closed semi-circle shape.

Yes, every closed plane shape has 1 face.

A line is one-dimensional. It has length but no depth, width, or curvature.

A closed 2D shape is a flat figure. It has no depth and no volume.