What is Triangle? Area of a Triangle Formula & Perimeter of a Triangle

What is Triangle?

In geometry, the triangle is the most popular topic and this is necessary to understand for early school students and competitive exam studies. So, what is a Triangle exactly? A Triangle is the most simpler form of a polygon having 3 sides or we can say that the triangle is a two-dimensional figure having three angles and 3 vertices. Also, keep in mind that sum of interior angles would make 180-degree while the sum of exterior angles should be 360-degrees. Let us have a quick look at properties of Triangle now.

  • The sum of interior angles of a triangle is 180 degrees.
  • The sum of exterior angles of a triangle would add up360 degrees.
  • The sum of the length of two sides would always be greater than the length of the third side. Similarly, the sum of angles of any sides would always be greater than the third side. Also, the difference of the two sides should always be less than the third side.
  • The smallest side of a Triangle would always be opposite to the shortest interior angle and the largest side would always be opposite to the longest interior angle.

Types of Triangles

In Geometry, Triangles are generally divided into multiple categories based on different attributes like side length or angles etc. Let us discuss on each of the types one by one in the section below.

Based on side length

  • Scalene Triangle– In this triangle, there are three different sides and three different angles that don’t match each other.
  • Isosceles Triangle–In this triangle, two sides and two opposite angles are equal. A famous isosceles theorem is based on the same concept.
  • Equilateral Triangle–As the name suggests, this type of triangle has all three sides equal in length and angles.

Based on Angles

  • Acute angled Triangle–In this triangle, all three angles should be less than 90-degrees.
  • Right angle Triangle– In this type of triangle, one angle should be of 90-degree.
  • Obtuse-angled Triangle– In this type of triangle, one angle should be greater than 90-degree.

Area of a Triangle Formula

For most of the shapes, we need to calculate the area and the perimeter. The area is defined as the region occupied within boundaries of an object or figure. The measurement of area is given in square units. For example, in case of meters, the area would be written as square meters.

To compute the areas of different shapes, there are predefined formulas and the same concept is true for a Triangle as well. For different types of triangle, the formula may be slightly different. Here, we will focus on a standard formula to compute the area of a Triangle as shown in the figure below –

\[\large Area\;of\;a\;Triangle = \frac{1}{2}ah \]
a is the base of the triangle.
h is the height of the triangle.

The Perimeter of a Triangle Formula

To calculate the perimeter of a Triangle, we generally take the sum of all sides of a shape and the same concept is applicable for Triangle as well.  Here, Perimeter of a Triangle formula would be given as –

\[\large Perimeter\;of\;a\;Triangle=a+b+c\]
Where a, b, and c are three different sides of a Triangle.