Geometry is one of the most important topic of mathematics which does deal with shapes and their properties. Dimension can be defined as a measure in a particular way. One dimensional measure will have only the measure of length. Two dimensional measure will have a measure of length and breadth. Three dimensional shapes will have length, breadth and height. There are even more dimensions in geometrical shapes but the most frequently used are two dimensional or 2D shapes. 2D shapes can be of different types such as circular, with three sides or more than three sides. These 2D shapes will lie on a plane and all these shapes will have a different property of their own.

A geometric shape having two dimensions is known as a 2D shape. This implies that this shape can be formed on a plane by moving the pen in any direction. If we draw a line on a plane it has to move only in one direction because a line is one dimensional. It can only have length. Now, if we draw a rectangle on a plane it will have length as well as breadth. Let us try the same with a cube. We cannot draw it on a plane as the cube will need a third dimension other than length and breadth, that is, height.Any shape having only two dimension can be called a 2D shape such as triangle, rectangle, pentagon, octagon, star and so on. The given figure shows some random images of 2D shapes.
2D Shapes
There can be various 2D shapes that can be drawn on a plane. The most common shapes can be classified as given here:
1) Shapes with three sides:

Triangle is the shape with three sides. Given are the various images of triangles.

List of 2D  Shapes
2) Shapes with four sides:

Quadrilaterals will have four sides. There are various kinds of quadrilateral as listed here.
  • Square
  • Rectangle
  • Parallelogram
  • Trapezium
  • Kite
  • Rhombus
Polygon

The above figure shows a polygon where the perpendicular distance between two sides is known as the height of polygon. Diagonal is the line between the two vertices of a quadrilateral. The given figure shows a diagonal.

Diagonal
3) Shapes with more than four sides:

    • Pentagon: 5 sides
    • Hexagon: 6 sides
    • Heptagon: 7 sides
    • Octagon: 8 sides
    • Nonagon: 9 sides
    • Decagon: 10 sides
4) Circular Shapes:

    Circle, ellipse and semicircle are various circular shapes. They can be drawn in a plane but they do not have an edge or a side.
Different 2D shapes will have different properties related to their area, perimeter, sides and angles between the sides. Some of the important properties of area, A, perimeter, P, length, l, and breadth, b, is given here. Length between two opposite sides is known as height of the quadrilateral.

 Shape  Perimeter  Area Special property
Image
Circle  2$\pi$r  $\pi r^{2}$ Locus is equidistant from center  
Circle

Square  4l  $l^{2}$ All sides equal
         Square
Rectangle  2(l+b)  $l\times b$  Angle between the sides is 90 degrees  Rectangle
Rhombus Sum of all sides  Half the product of two diagonals  Diagonals are equal and all sides are equal           Rhombus
Trapezium Sum of all sides  $\frac{1}{1}$ $\times\ Sum\ of\ parallel\ sides\ \times\ height$  Two sides are parallel.           Trapezoid
Parallelogram Sum of all sides  $length\ of\ one\ side\ \times\ perpendicular\ distance\ between\ two\ parallel\ sides$
 Opposite sides are equal and parallel to each other.  Parallelogram
Triangle Sum of all sides  $\frac{1}{2}$ $\times\ Base \times\ Height$  There are various types and properties of triangles.  Triangle
Example 1:

If length of a square is given 10 units then what will be its breadth?

Solution:

In a square, length will be equal to breadth. Hence, breadth of the square will also be 10 units.
Example 2:

If perimeter of a parallelogram is given as 16 meters and height is 5 meters then find its area.

Solution:

Perimeter is sum of all sides. For a parallelogram all sides are equal. Hence, if one side is taken as l then,
   
4l = 16 which gives l = 4

Area = $\frac{1}{2}$ $l\ \times\ height$
       
        = $\frac{1}{2}$ $4\ \times\ 5$

        = $10$

Area of this parallelogram is 10 square meters.
Example 3:

For a triangle ABC the base length is given to be 10 meters and area is of 250 square meters. Find the altitude of the triangle.

Solution:

Area of ABC = $\frac{1}{2}$ $\times\ Base\ \times\ Height$

Now, from the given information base = 10 and area = 250.

Hence, 250 = $\frac{1}{2}$ $\times\ 10\ \times\ Height$

Height = $\frac {250 \times 2}{10}$ = $50$.

The height or the altitude of the triangle ABC is 50 meters.