Fast Fact
The field of geometry and associated studies of shapes and figures reportedly originated first in the Indus River Civilization and the Babylonian Civilization around 3000 BC. Several reports suggest that the Egyptians had their own version of the Pythagorean theorem even before Pythagoras formulated it.
The appearance or form of an object or a body which remains stable or is constant under specific normal conditions is called the geometric shape of that object. Simply said, geometric shapes are characterized as the external orientations of the objects under consideration. As the parameters differ, so do the shape types. If the shapes of two objects are same or similar, they are said to be congruent to each other. Any known body or materialistic entity in the entire universe can be said to be present in the form of a geometric shape.
Basically, there are two types of geometric shapes: two dimensional (2D) and three dimensional (3D). The former can be drawn with reference to the X and Y axes, whereas, the latter also includes the Z axis. 2D shapes and figures mainly consist of points and connecting lines, which form the shape. They can either be convex (regular appearance) or concave (irregular) appearance. In many polygonal 2D figures, the convex ones have angles less than 180 degrees, whereas, the concave shapes have at least one angle greater than 180 degrees. 3D figures are more complex, and consist mainly of vertices, edges, faces, etc.
INDEX
Two Dimensional (2D) Shapes
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Triangles
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Quadrilaterals
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Polygons
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Curved Shapes
Three Dimensional (3D) Shapes
The following sections will help you understand the meaning of basic geometric figures, along with their pictures. Note that all the angles mentioned are the interior ones.
Different Types of Geometric Shapes
Two Dimensional (2D) Shapes
Triangles
This is a type of polygon that consists of three sides with three apexes. The sum of the angles of a triangle is equal to 180 degrees in any type. Refer to the section below for more details.
Isosceles Triangle
Two sides have equal length, and two angles are also equal. Line of symmetry is present.
Scalene Triangle
Length of all sides is unequal, and all three angles have varying values.
Equilateral Triangle
All three sides and angles are equal. Line of symmetry is present.
Right Triangle
One of the angles is 90 degrees. Line of symmetry may or may not be present.
Obtuse Triangle
One of the angles is greater than 90 degrees. Line of symmetry may or may not be present.
Acute Triangle
All angles are acute (less than 90 degrees). Line of symmetry may or may not be present.
Quadrilaterals
These polygons consist of four sides, and the sum of the angles is equal to 360 degrees in any type. Refer to the section below for more details.
Rectangle
They have two sets of opposite sides that are equal, and all four angles are 90 degrees. Two lines of symmetry are present.
Square
All four angles are equal to 90 degrees, along with four equal sides. This polygon has four lines of symmetry.
Parallelogram
They consist of two sets of opposite lines that are equal and parallel. The opposite angles are also equal regarding any value. Line of symmetry may be present.
Rhombus
All four sides are equal and parallel, but only opposite angles are equal. Two lines of symmetry are present. It is closely related to the square and parallelogram.
Trapezoid
One set of opposite lines is parallel and the other set is non-parallel. Line of symmetry may be present. It is called a Trapezium in the UK.
Trapezium
All four sides are unequal and non-parallel, and the line of symmetry is absent. It is called a Trapezoid in the UK.
Kite
Two sets of adjacent sides are equal, and two opposite angles also have equal values. Line of symmetry is present.
Irregular Quadrilateral
It has four unequal sides, and the appearance is concave, i.e., at least one angle is greater than 180 degrees.
Polygons
The figures that consist of three or more than three sides are known as polygons. The angles of such kind of geometric shapes may be more than 360 degrees. Both regular and irregular types of polygons are given below.
Note: Though Triangle and Quadrilateral types are included under Polygons, as they have been described above, they are not listed in the following section.
Pentagon
It consists of five equal sides, and the sum of the angles is equal to 540 degrees. Five lines of symmetry are present.
Hexagon
It consists of six equal sides, and sum of the angles is equal to 720 degrees. Six lines of symmetry are present.
Heptagon
It consists of seven equal sides, and the sum of the angles is equal to 900 degrees. Seven lines of symmetry are present.
Octagon
It consists of eight equal sides, and sum of the angles is equal to 1080 degrees. Eight lines of symmetry are present.
Nonagon
It consists of nine equal sides, and sum of the angles is equal to 1260 degrees. Nine lines of symmetry are present.
Decagon
It consists of ten equal sides, and sum of the angles is equal to 1440 degrees. Ten lines of symmetry are present.
Dodecagon
It consists of twelve equal sides, and sum of the angles is equal to 1800 degrees. Twelve lines of symmetry are present.
Irregular Polygon
It may have four or more than four unequal sides, and the appearance might be concave, i.e., at least one angle is greater than 180 degrees.
Curved Shapes
The figures that consist of curved lines and associated points are called curved shapes. The main types that are included under this category are described below:
Circle
Consisting of only one curved line, this shape does not have any other joining point or apex. The distance from the epicenter to the circumference is equal throughout all the sectors.
Oval/Ellipse
It is similar to the circle, but the distance from the center to the circumference varies constantly. Thus, this shape has two axes: major and minor, along with an elongated shape.
Lens
This figure is similar to an ellipse, but consists of two distinct curved lines that meet at opposite ends. In this case, two points are present at their junction.
Crescent
This shape is characterized by the presence of two curved lines: one is convex and the other is concave. They meet in a similar manner as that of the lens, forming a peculiar figure.
Arches
These figures consist of a curved line that meets a straight line at two adjacent points. The former line may be entirely curved or might be in the form of two parallel lines before joining the straight line.
Annulus
This figure is characterized by the presence of two concentric circular structures, both of which differ in size. In most cases, the interior of the shape is not closed. This figure is also called a ring structure.
Circular Segment
It is mainly defined as a part of a circle, that may consist of a portion of the circumference, along with a chord. The shape may be a semicircle or might be a figure with minimum circumference portion. The remaining part may also be called a segment.
Circular Sector
It is mainly defined as the triangular portion that is marked by a portion of circular circumference and two straight lines. The latter meet at a common point, mostly at the circle center. They remaining half of the circle can also be called a sector.
The shapes described above are the basic ones, and apart from these, numerous other figures exist in the category of 2D geometry. After going through these shapes, let's take a look at the different kinds of geometric figures that come under the 3D category.
Three Dimensional (3D) Shapes
Cube/Hexahedron
This figure has 12 edges, 8 vertices, and 6 faces. The sides are all equal in length and the faces are square-shaped.
Rectangular Prism/Cuboid
It has the same features as that of the cube regarding number of sides, faces, and vertices, except that the faces are rectangular in shape.
Cylinder
This shape does not have any vertices, but consists of two flat faces (only in case of a closed cylinder), and one curved face. Two edges are also present.
Sphere
This geometric figure does not have any edges and vertices, and only one curved face is present. It is the most evenly curved shape included under the 3D category.
Triangular Prism
It consists of six vertices, nine edges, and five faces. Faces at either end are triangular in shape, whereas, all the other ones are rectangular in shape.
Cone
Along with one apex and one edge, cones have one curved face, and one additional flat face (in closed cones). The angle of the apex may vary from acute to obtuse.
Hexagonal Prism
Consisting of twelve vertices, eighteen edges, and eight faces, this figure has two hexagons at the opposite ends. The remaining faces have a rectangular or square shape.
Pentagonal Prism
Consisting of ten vertices, fifteen edges, and seven faces, this figure has two pentagons at the opposite ends. The remaining faces have a rectangular or square shape.
Square Pyramid
In this shape, the base is made up of a square, whereas, the rest of the faces are triangles. Overall, it has 5 vertices, 8 edges, and 5 faces.
Triangular Pyramid
In this shape, the base as well all the faces are triangles. Overall, it has 4 vertices, 6 edges, and 4 faces. The basal triangle has a different size as compared to the faces.
Hexagonal Pyramid
This shape consists mainly of 7 vertices, 12 edges, and 7 faces. Its base is hexagonal in shape, and the faces are triangular.
Parallelepiped
In this figure, all the faces as well as the base are in the shape of parallelograms. The sizes of the faces may differ or may be same.
Tetrahedron
It is similar to the appearance of a triangular pyramid, with the only exception being that all the face sides and the base are all of equal size.
Octahedron
This figure has eight triangles arranged in a specific manner to form six vertices, eight faces, and twelve edges. The triangles may be either equilateral or isosceles.
Dodecahedron
They consist of twelve pentagonal faces, twenty vertices, and 30 edges. The faces are of equal-sized pentagons.
Icosahedron
They are characterized by 30 edges, 20 faces, and 12 vertices. The faces are made up of equilateral triangles.
Rhombic Dodecahedron
This type of figure consists of 12 rhomb-shaped faces, along with 14 vertices and 24 edges.
Frustum
It is a cone-shaped structure, but instead of an apex, a circle is present at one end.
A comprehensive knowledge of geometric shapes and figures is very important, especially if one has an inclination towards this sub-field of mathematics. Also, one must learn to follow the different mathematical rules that are needed while drawing geometrical shapes. The figures described above, along with the sample equations, will surely help you to clear your basics about this topic.
