## AREA OF SCALENE TRIANGLE

Area of scalene triangle :

Here 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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