There are three sides in a triangle. The height  of the triangle can be calculated in different ways. It is all depends on the information provided in the question. Height is the measurement of  vertical distance. Perpendicular distance from a vertex to the opposite side of a triangle is called height.


Calculation of height of a Triangle


Height of the triangle can be calculated according to information provided :

 For Right angle triangle:

Using Pythagorean theorem: According to this theorem square of hypotenuse is equal to the sum of squares of its two sides.

Let the sides are B and P and Hypotenuse  H       

here P is the height of the triangle                                              

then according to Pythagorean theorem

 H2 = B2 + P2

P2 =   H2   -  B2

(height of the triangle)2 = (Hypotenuse)2 - (Base)2

This way we find the square of height.

Now take the square root.

(height of the triangle)  = √ Hypotenuse2 - Base2


Right angel Triangle

Find the height of the given figure?                                                                            

This is a right angle triangle.                                              

here b = 3, H = 5

height of the triangle= √ Hypotenuse2 - Base2

           h   = √ 52 - 32

           h = √ 16          h = 4 unit


For any triangle


Following formula is used.

Area of the triangle = 1/2 x base x height

height = (2 x Area of the triangle )/ base


Calculate the height of the triangle if the area is 150 cm2  and base is 12cm.

using the formula      

Area of a Triangle                                                                                            

Area of the triangle = 1/2 x base x height                                             

                      150     = 1/2 x 12 x h

                     150   = 6x h

           `rArr`      150/6 = h

                        25 =  h

                         h = 25 cm.

For different base , corresponding height is different. In above example , height h is corresponding to base 12.


height of an equilateral triangle


Equilateral  triangles are the triangles having all sides of same length.

height of an equilateral triangle =  `sqrt(3)` / 2 x side