Plane Shapes – Definition, Types, Solved Examples, Facts, FAQs

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What Are Plane Shapes?

In geometry, plane figures or plane shapes, also known as two-dimensional shapes, are fundamental geometric figures that exist in a flat, two-dimensional plane.

Plane shapes do not have thickness or depth unlike three-dimensional shapes, making them ideal for representation on a flat surface, such as a piece of paper. These shapes are the building blocks of geometry and are extensively studied in mathematics.

Plane shapes examples

Definition of Plane Shape

Plane shapes can be defined as two-dimensional geometric figures that exist on a flat surface, known as a plane. 

These shapes have only length and width, with no depth or thickness. They are characterized by their boundaries, which can be made up of straight sides or curved lines. Plane shapes examples include polygons (triangles, quadrilaterals), circles, and other curvilinear figures. 

Different Plane Shapes in Geometry

In geometry, there are several different types of plane shapes. Here are some of the most commonly discussed ones:

TrianglesTriangles are closed plane shapes with three sides and three angles. Triangle
QuadrilateralsQuadrilaterals are closed plane shapes with four sides and four angles. Common examples are squares, rectangles, and parallelograms.Quadrilaterals
CirclesCircles are plane shapes with a curved boundary consisting of all points equidistant from a fixed point called the center.Circle
OvalsOval shape is a plane shape that resembles the shape of an egg or a squashed circle.Oval shape
Different PolygonsPolygons are closed plane shapes with at least three sides.
Polygons with three sides: TrianglesPolygons with four sides: QuadrilateralsPolygons with five sides: PentagonsPolygons with six sides: Hexagonsetc.

Polygons

What Are Open and Closed Shapes?

In geometry, plane shapes can be categorized as open or closed based on their boundaries.

  1. Closed Plane Shapes: Closed shapes are plane figures that have a complete and continuous boundary that forms a closed loop. This means that the shape does not have any openings (holes) or breaks in its boundary. 

Examples of closed plane shapes include polygons (such as triangles, squares, pentagons), circles, ellipses, etc. These shapes enclose a finite area within their boundaries.

Examples of closed shapes
  1. Open Plane Shapes: Open shapes are figures that do not have a complete and continuous boundary. They have one or more openings or breaks in their boundary, which means they do not form a closed loop. 

Examples of open plane shapes include lines, line segments, rays, and curves that do not form closed loops (like a curve with endpoints that do not meet). Open plane shapes do not enclose any area since they lack a complete boundary.

Examples of open shapes

Polygons

Polygons are most commonly discussed plane shapes apart from circles.

In geometry, a polygon can be defined as a flat or plane, two-dimensional closed shape bounded with at least three sides. 

It does not have curved sides. The sides of a polygon are also called its edges. The points where two sides meet are the vertices (or corners) of a polygon.

The types of polygons can be categorized into three major forms: regular or irregular, concave or convex, and simple or complex. 

Regular Polygons and Irregular Polygons:

Regular PolygonsIrregular Polygons  
A regular polygon has all sides of equal length and all interior angles of equal measure. Examples include equilateral triangles, squares, and regular pentagons.An irregular polygon has sides of different lengths and/or interior angles of different measures. Examples include scalene triangles, rectangles, and irregular hexagons.

Regular polygons

Irregular polygons

Convex Polygons and Concave Polygons:

Convex PolygonsConcave Polygons
A convex polygon has all its interior angles less than 180 degrees. All sides of a convex polygon lie on the same side when any two points inside the polygon are connected. Examples include equilateral triangles, squares, and regular hexagons.A concave polygon has at least one interior angle greater than 180 degrees. It has at least one “caved-in” or “dented” portion. Examples include a star shape or a crescent shape.
Convex polygonConcave polygon

Simple Polygons and Complex Polygons

Simple PolygonsComplex Polygons
A simple polygon is non-self-intersecting, meaning that its sides do not cross over each other. It forms a single continuous shape. Examples include triangles, rectangles, and regular polygons.A complex polygon is self-intersecting, meaning that it has sides that cross over each other, creating additional interior regions within the polygon. Examples include shapes with holes or overlapping sides.
Simple polygonsComplex polygons 

Sides and Vertices of Plane Shapes

Sides: In plane shapes, the sides refer to the straight line segments that form the boundary of the shape.

Vertices: The corners or the points where the sides meet are called the vertices. 

It’s important to note that some plane shapes, such as circles, do not have straight sides or corners/vertices. Instead, they have a continuous curved boundary. However, polygons are the plane shapes that have distinct sides and corners/vertices that define their structure.

Sides and corners of shapes

No sides, No Corners

Plane Shapes vs. 3D Shapes

AspectPlane Shapes3D Shapes
DimensionsTwo-dimensionalThree-dimensional
Flat or SolidFlat, occupy a single planeSolid, occupy space
DepthNo depth or thicknessHave depth and thickness
ExamplesTriangles, rectangles, circlesCubes, spheres, cylinders
VolumeNo volume, as they are flatHave volume, representing the amount of space they occupy
ProjectionRepresented on a flat surfaceMay have different views from different angles

Facts about Plane Shapes

  • Plane shapes, also known as 2D shapes, are flat figures that exist in a two-dimensional space, with length and width but no depth.
  • A polygon is a closed plane figure with straight sides. Examples of polygons include triangles, quadrilaterals, pentagons, hexagons, and so on.
  • Circles are another type of plane shape. They are perfectly round and have no straight sides or angles. Circles are not polygons.

Conclusion

In this article, we have learned about plane shapes. Learning about plane shapes provides a solid foundation for geometry, enhances problem-solving skills, and has practical applications in numerous fields. It promotes critical thinking, spatial reasoning, and effective communication, making it both useful and necessary in education and beyond. Now let’s solve some examples and practice problems for better understanding.

Solved Examples on Plane Shapes

Example 1: Classify the following plane shape as open, closed, simple, or complex.

A complex shape

Solution: 

The shape crosses itself. 

So, it is not simple. It is a complex shape.

It forms a closed loop. 

So, it is a closed shape. It is not an open shape.

Example 2: Which of the following are not plane shapes?

Circle, Sphere, Cube, Square, Cuboid, Triangle

Solution:

Sphere, cube, cuboid are 3D shapes or geometric solids.

So, they are not plane shapes.

Circle, square, triangle are plane shapes.

Example 3:  Which of the following is not an open shape?

Identifying open and closed shapes

Solution: 

Shapes a, b, and c have different starting and end points. They do not have any interior.  

The shape d does not have any open ends, so it is a closed shape. It forms a closed loop and has an interior.

Example 4: How many sides, vertices does this shape have? Is the shape closed or open? 

A plane shape

Solution: 

First, we count the number of straight line segments in the shape.

There are eight straight lines connected to each other, making an octagon. 

As this octagon’s outline may be traced without any gaps, it is a closed shape.

Practice Problems on Plane Shapes

Plane Shapes - Definition, Types, Solved Examples, Facts, FAQs

Attend this quiz & Test your knowledge.

1

What are plane shapes in mathematics?

Any closed, flat, 2-dimensional shape
Any open, or closed flat, 2-dimensional shape
Any closed, 3-dimensional shape
All shapes are plane shapes.
CorrectIncorrect
Correct answer is: Any open, or closed flat, 2-dimensional shape
Plane shapes, also known as two-dimensional shapes, are fundamental geometric figures that exist in a flat, two-dimensional plane.
2

Which plane shape has no sides?

Triangle
Square
Circle
Hexagon
CorrectIncorrect
Correct answer is: Circle
A circle is a plane shape with a curved boundary and no sides. It consists of all points equidistant from a center point.
3

Which shape has three sides and three angles that add up to 180 degrees?

Triangle
Square
Rectangle
Pentagon
CorrectIncorrect
Correct answer is: Triangle
A triangle is a polygon with three sides and three angles. The sum of the interior angles of any triangle always adds up to 180 degrees.
4

What do we call plane shapes with four sides?

pentagon
quadrilateral
hexagon
circle
CorrectIncorrect
Correct answer is: quadrilateral
A pentagon has 5 sides, a hexagon has 6 sides, while a circle is a curved figure with no straight sides. Therefore, the term used to describe plane shapes with four sides specifically is a quadrilateral.
5

Which of the following is an open shape?

Plane Shapes – Definition, Types, Solved Examples, Facts, FAQs
a
b
c
d
CorrectIncorrect
Correct answer is: b
Figure b has different starting and ending points. Therefore, it is an open shape.

Frequently Asked Questions about Plane Shapes

Symmetry refers to the balanced arrangement of elements. Plane shapes can exhibit symmetry, such as line symmetry (mirror image) or rotational symmetry (ability to rotate around a central point and maintain the same appearance).

Plane shapes have various applications in real life, including architecture and design (floor plans, blueprints), art (paintings, sculptures, tessellations), map projections, and more.

Congruent shapes are identical in shape and size, while similar shapes have the same shape but can differ in size.

Plane shapes are two-dimensional and can be considered as the faces of three-dimensional shapes. Three-dimensional shapes are composed of plane shapes interconnected in a three-dimensional space.

A polygon is a two-dimensional plane shape with straight sides, while a polyhedron is a three-dimensional solid shape with flat polygonal faces, edges, and vertices.

The area of a plane shape refers to the measure of the space enclosed within its boundaries, while the perimeter is the total length of its boundary. There is no direct relationship between the area and perimeter of a shape; they are separate measurements used to describe different aspects of the shape.

Two plane shapes are similar if their corresponding angles are equal, and the ratios of their corresponding side lengths are proportional.

Flat shapes and plane shapes refer to the same concept.Both terms are used interchangeably to describe two-dimensional figures that exist on a flat surface or plane. These shapes have length and width but no depth.