Area of scalene triangle :
Here we are going to see the formulas and example problems to find the area of the scalene triangle.
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.
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
The sides of a triangle are 12m, 16 m and 20 m. Find the altitude to the longest side.
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
= 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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