Types of Triangles
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All triangles have 3 sides and 3 angles which always add up to 180°.

The Triangle Inequality Theorem states that:
  The longest side of any triangle must be
  less than the sum of the other 2 sides.

Triangles are classified in 2 ways-

1) By the number of equal sides they have:
  • scalene - all 3 sides have different lengths
  • isosceles - 2 sides have equal lengths
  • equilateral - all 3 sides are equal

2) By the types of angles they have:
  • acute triangle - all 3 angles are acute (less than 90°)
  • right triangle - has one right angle (a right angle = 90°)
  • obtuse triangle - has one obtuse angle (an obtuse angle is greater than 90° and less than 180°).

When these 2 categories are combined, there are 7 possible triangles:
  • acute scalene (diagram A)
  • right scalene (B) - all right triangles are scalene (except diagram E).
  • obtuse scalene (C)


  • acute isosceles (diagram D)
  • right isosceles (E) also known as a 45° 45° 90° triangle.
  • obtuse isosceles (F)


  • equilateral (G) all sides are equal and each angle = 60°, making this the only equiangular triangle. Since all 3 angles are less than 90° all equilateral triangles are acute triangles.


There is one more type of triangle that is worth mentioning.
An oblique triangle is any triangle that is not a right triangle.


Triangle Area Formulas

The most well-known triangle area formula is multiplying the length of the base by the height (also called the altitude), and dividing that by 2.


If you know the length of all 3 sides of a triangle, you can calculate the area by using Heron's Formula (sometimes called Hero's Formula).
First we have to define a triangle's perimeter which is (side a + side b + side c).
A triangle's semi-perimeter (or 's') is one half of the perimeter or to put it another way:

semi-perimeter = (side a + side b + side c) ÷ 2

Example: A triangle has side a = 4, side b = 5 and side c = 6. What is its area?
The perimeter = 4 + 5 + 6 = 15.
The semi-perimeter is one half of this or 7.5
Using Heron's formula,
area = square root (s • (s - 4) • (s - 5) • (s - 6))
area = square root (7.5 • (7.5 - 4) • (7.5 - 5) • (7.5 - 6))
area = square root (7.5 • (3.5) • (2.5) • (1.5))
area = square root (98.4375)
area = 9.921567416...

Triangle Area Calculator

This calculator determines triangle area by using either of the 2 methods above.
If you need a more advanced triangle calculator then click here.

   

 
 
 


 


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