What are two dimensional shapes?
Two-dimensional shapes, as the name suggests, are shapes that have two dimensions—length and width. In other words, two-dimensional shapes are shapes that don’t have depth or height. We can draw two-dimensional shapes on flat planes such as a piece of paper, a blackboard and so on. Triangles, circles, squares and rectangles are some examples of two-dimensional shapes.
Sides and Vertices of two dimensional shapes
Vertex: Vertices are points that form the corners of a shape. It is the point of intersection where two or more sides meet. For a two-dimensional shape, the number of vertices is always equal to the number of sides.
So, a triangle—a three-sided shape—has three vertices, and a quadrilateral—a four-sided shape— has four vertices.
Sides: The lines that join two vertices of a two-dimensional figure are known as the sides of the shape. The length of a side is the distance between two vertices or the points of intersection. Shapes can be categorized based on the number of sides they have. Three-sided shapes are known as triangles, four-sided shapes are known as quadrilaterals, five-sided shapes are known as pentagons, and so on.
The three-sided shape in the figure is known as a triangle and the four-sided shape is known as a quadrilateral
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Types of two-dimensional shapes
There are two types of two-dimensional shapes: open and closed two-dimensional shapes.
Closed shapes
Closed shapes are those shapes that are enclosed from all sides and have no openings. A closed shape does not have any openings in its boundary. All sides of the shape connect to other sides to form vertices. They start and end at the same point. In other words, we can draw a closed shape without lifting the pen from paper.
Open shapes
Open shapes are the shapes whose line segments do not meet to enclose the shape. If a two-dimensional shape has at least one line segment that does not join a vertex, the shape will be an open shape. They don’t start and end at the same point.
Sorting Shapes
Shapes can be classified based on: (partitioning shapes)
The number of sides
The number of vertices
Whether the shape is open or closed.
Let’s understand how to sort shapes based on a specific criteria using an example below.
Example: Circle the closed shapes with 4 vertices.
We need to pick closed shapes with 4 vertices. That means the shapes should have no gaps in their sides and they need to have 4 vertices as well.
So we have 4 shapes that fit this criteria.
Describe two-dimensional shapes
Triangles, rectangles, squares, trapezoids and so on, are some examples of two-dimensional shapes. The sides and vertices of these shapes are,
Triangle: A triangle has 3 straight sides and 3 vertices.
Rectangle: A rectangle has 4 straight sides and 4 vertices.
Square: A square has 4 sides and 4 vertices. All 4 sides of a square are equal in length.
Hexagon: A hexagon has 6 sides and 6 vertices. A regular hexagon has 6 sides of equal length.
Rhombus: A rhombus has 4 equal sides and 4 vertices.
Trapezoid: A trapezoid has 4 straight sides and 4 vertices.
Solved Examples
Example 1: Which of the figures shown below are closed shapes?
Solution:
a) The circle shown here has no break in its boundary. So, it is a closed figure.
b) The next figure does not have a continuous boundary. It is an open figure.
c) This figure, like the one before, is open at one of its sides. So, it is not a closed figure.
d) The figure is a rectangle. All of its sides are closed. So, it is a closed figure.
Example 2: Which of these shapes have 4 straight sides?
Solution:
a) The figure is a hexagon. It has 6 sides.
b) The given shape is a rectangle.
So, it has 4 sides.
c) It is a square.
So, it has 4 sides.
d) It is a trapezoid.
So, it has 4 sides.
e) The figure is a triangle. It has only 3 sides.
f) The figure is a pentagon. It has 5 sides.
Example 3: Match shapes with their attributes.
Solution:
In the left column, we have a hexagon, square and circle. In the right column, we have 0 vertices, 6 straight sides and only 4 sides. We need to match the shapes with the right feature or attribute.
By counting the number of sides and vertices of the hexagon, we know that the hexagon has 6 sides and 6 vertices. Hence, the hexagon is matched to ‘6 straight sides’.
Similarly, a square has 4 vertices and 4 sides. Hence, it is matched to ‘4 sides’.
We know that a circle does not have a vertex. Hence, the circle is matched to ‘0 vertices’.
Example 4: Sort the following shapes according to the increasing order of number of sides and vertices.
Solution:
D has three sides and three vertices, B has four sides and four vertices, A has five sides and five vertices, and C has six sides and six vertices.
The increasing order of sides and vertices among the given shapes:
D < B < A < C
Flat surfaces are also known as planes. It is a horizontal surface which has no depth or height. It only has length and breadth. The flat surfaces do not have any curvature or bending. Pieces of paper, screens of our laptop and cell phones are examples of flat surfaces.
A shape that has 4 straight sides is called a quadrilateral. For example; squares, rectangles and trapezoids are all quadrilaterals.