area of scalene triangle

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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