Area of Scalene Triangle

In this page area of scalene triangle we are going to see the formulas and example problems to find the area of the scalene-triangle.

Formula :

Area of scalene triangle = √s(s-a)(s-b)(s-c)

Here a, b and c are the sides of the triangle and "s" is known as (perimeter of the triangle)/2. To find the value of "s" we have to use the formula

 S = (a + b + c)/2 

Now let us see some example problems.

Example 1:

Find the area of the scalene triangle whose length of sides are 12cm, 18 cm and 20 cm.

Solution:

Here we can consider the length of each side as a= 12 cm, b = 18 cm and c = 20 cm respectively.

First,let us find the value of s. For that let us use the above formula

 S = (a + b + c)/2

S= (12 + 18 + 20)/2

S = 50/2

S = 25

Area of scalene-triangle = √s(s-a)(s-b)(s-c)

                                                  = √25(25-12) (25-18) (25-20)

                                                  = √25(13) (7) (5)

                                                 =  √5 x 5 x 13 x 7 x 5

                                                 = 5 √13 x 7 x 5

                                                 = 5√455 cm²


Example 2:

The sides of a triangle are 12m, 16 m and 20 m. Find the altitude to the longest side.

Solution:

In order to find the altitude on the longest side of a triangle first we have to find the area of the triangle.

Let a = 12 m, b = 16 m and c = 20 m

          S = (a + b + c) /2

             = (12 + 16 + 20)/2

             = 48/2

             = 24 m

Area of scalene triangle = √s(s-a) (s-b) (s-c)

                       = √24 (24-12) (24-16) (24-20)

                       = √24 (12) (8) (4)                                              

                       = √2 x 12 x 12 x 4 x 2 x 4

                       = 12 x 2 x 4  

                       = 96 cm²

Area of the triangle = 96 cm²

(1/2) x b x h = 96 cm²

Here the longest side is 20 cm. If we plug it instead of b we will get

(1/2) x 20 x h = 96

                h = (96 x 2) /20

                h = 9.6 cm  


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Area of Scalene Triangle to Formulas for Shapes