Overview: Polygons | Quantitative Aptitude for SSC CGL PDF Download

Polygon Definition

Well acknowledged with the definition, let us take a step forward with the various types and learn about them.

Triangles (3 Sided Polygon)

One of the basic properties of a triangle is that the total sum of the internal angle of a triangle is equal to 180 degrees and depending on the sides, angles and vertices they are classified as follows:

A triangle with all the sides equal is called an equilateral triangle. Consider, ∆ABC; for the triangle to be an equilateral triangle the condition of the sides is; AB = BC = CA, and each angle should be equal to 60 degrees that is ∠A = ∠B = ∠C = 60°.

Isosceles Triangle

A triangle is termed an isosceles triangle whose two sides are equal. Consider a ∆ABC is an isosceles triangle then AB = AC in addition to this angles opposite to equal sides are equal i.e. in the figure shown below ∠B = ∠C.

Scalene Triangle

A triangle whose all three sides are different or unequal in length is called a scalene triangle.

Right Angle Triangle

A triangle whose one angle is 90° is called a right-angled triangle. Here, ∆ABC is a right-angled triangle because ∠C = 90°.

• Triangles can be classified based on their angles into acute-angled triangles (with angles less than 90°) and obtuse-angled triangles (with an angle greater than 90°).
• This classification will be covered in detail in a separate article on triangles.

Quadrilateral (4 Sided Polygon)

Any four non-collinear points form a quadrilateral; the quadrilateral has multiple names depending on the shape. Some of the important ones are discussed below:

Parallelogram

In a parallelogram figure, opposite sides are parallel and identical with diagonals bisecting each other. Also, the summation of two adjacent angles is 180 degrees.

Rectangle

In a rectangle, opposite sides are parallel and equivalent with diagonals bisecting each other. Also, all the angles in a rectangle are equal and the summation of the adjacent angles is equal to 180 degrees.

Square

In a square all the four sides are equal and the opposite side is parallel to one another with diagonals bisecting each other. Along with this, all the angles are of the same measure i.e. 90 degrees.

Rhombus

In a rhombus all the four sides are equal and the opposite side is parallel to one another with diagonals bisecting one another. The measures of the angles are different but the opposite angles are equal.

Trapezium

In a trapezium, all sides are of different lengths in such a way that one pair of opposite sides is parallel. There is nothing certain about the angles, or diagonals of a trapezium.

Other Polygons

Area and Perimeter of Polygons

The perimeter can be understood as the total distance surrounded by the border of any two-dimensional shape. The perimeter of some regularly used polygons are listed below:

• The perimeter of a triangle is simply the entire length of the outer boundary of the triangle that is equal to; Total sum of all Sides.
• The perimeter of the parallelogram = 2 × (sum of lengths of adjacent sides).
• Perimeter of the square = 4a (a=side length).
• The perimeter of a rhombus =4x (x=side length)
• Perimeter of a rectangle = 2 x (L + B)

The area is the total room occupied by them. The area of the polygon formula depends upon the number of sides and the classification as well. The area formula for some commonly used shapes are:

• Area of triangle =1/2 × Base × Height.
• Area of the parallelogram = (base x height).
• Area of the square= a2$𝑎2$.
• The area of a rhombus =12×d1×d2$\frac{1}{2}\times 𝑑1\times 𝑑2$. Here d1 and d2$𝑑1𝑑2$ are the length of two diagonals of the rhombus.
• Area of a rectangle = Length × Breadth.