HERON'S FORMULA TO FIND AREA OF TRIANGLE
Scalene triangle is a triangle with all sides of different lengths.
All angles are different, too.
So no sides are equal and no angles are equal.
We can use Heron's formula to find area of a scalene triangle.
Heron's Formula for Area of Scalene Triangle :
= √[s(s - a)(s - b)(s - c)]
where
S = (a + b + c) / 2
Here a, b and c are side lengths of the triangle.
Practice Problems
Problem 1 :
Using Heron’s formula to find the area of a triangle whose side lengths are
10 cm, 24 cm and 26 cm
Solution :
a = 10 cm, b = 24 cm and c = 26 cm
s = (a + b + c)/2
s = (10 + 24 + 26)/2
s = 60/2 = 30
s - a = 30 - 10 = 20
s - b = 30 - 24 = 6
s - c = 30 - 26 = 4
√s(s − a)(s − b)(s − c) = √30(20)(6)(4)
= 120 cm2
Problem 2 :
Using Heron’s formula to find the area of a triangle whose side lengths are
1.8 m, 8 m, and 8.2 m
Solution :
a = 1.8 m, b = 8 m and c = 8.2 m
s = (a + b + c)/2
s = (1.8 + 8 + 8.2)/2
s = 18/2 = 9
s - a = 9 - 1.8 = 7.2
s - b = 9 - 8 = 1
s - c = 9 - 8.2 = 0.8
√s(s − a)(s − b)(s − c) = √9(7.2)(1)(0.8)
= 7.2 m2
Problem 3 :
The sides of the triangular ground are 22 m, 120 m and 122 m. Find the area and cost of levelling the ground at the rate of ₹ 20 per m2.
Solution :
a = 22 m, b = 120 m and c = 122 m
s = (a + b + c)/2
s = (22 + 120 + 122)/2
s = 264/2 = 132
s - a = 132 - 22 = 110
s - b = 132 - 120 = 12
s - c = 132 - 122 = 10
√s(s − a)(s − b)(s − c) = √132(110)(12)(10)
= √(11 ⋅ 12 ⋅ 11 ⋅ 10 ⋅ 12 ⋅ 10)
= 11 ⋅ 12 ⋅ 10
= 1320 m2
Cost of leveling the ground = ₹ 20 per m2.
Required cost = 20(1320)
= ₹ 26400
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