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Based Upon Sides

  1. Scalene triangle
A triangle whose all sides are of a different length is a scalene triangle.
 
 
Area Description: 7346.png where
 
S (semi perimeter) Description: 7339.png
 
Example
What is the area of the triangle with side lengths 4 units, 5 units and 10 units?
Solution
This triangle is not possible. (Since the sum of lengths of the two sides > Length of the third side)
 
  1. Isosceles triangle
A triangle whose two sides are of an equal length is an isosceles triangle.
 
Height Description: 7332.png
 
Area Description: 7323.png
  1. Equilateral triangle
A triangle whose all sides are of an equal length is called an equilateral triangle.
Description: P-322-1.tif

In any equilateral triangle, all the three sides are of an equal length, so a = b = c
 
Height = (side) Description: 7308.png
 
Area Description: 27965.png

Based Upon Angles

  1. Right-angled triangle
A triangle whose one angle is of 90° is called a right-angled triangle. The side opposite to the right angle is called the hypotenuse.
Description: P-322-2.tif 
 
Area Description: 7286.png × base × perpendicular
  1. Obtuse-angled triangle
If one of the angles of the triangle is more than 90°, then the triangle is known as an Obtuse angled triangle. Obviously in this case, rest of the two angles will be less than 90°.
  1. Acute-angled triangle
If all the angles of the triangle are less than 90°, then the triangle is known as acute angled triangle.
  1. Isosceles right-angled triangle
A right angled triangle whose two sides containing the right angle are equal in length, is an isosceles right tri­angle.
 
Description: P-324-4.tif
 
In this case, Hypotenuse (h) Description: 7157.png
 
Perimeter = 2a + h = 2a + Description: 7150.png
Description: 7143.png 
Description: 7136.png 
= Hypotenuse Description: 7129.png




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