Heron's Formula
The area of a triangle can be calculated by using Heron's formula if we only know the length of all three sides of the triangle.
Let's learn more about Heron's formula with a few solved examples.
What Is Heron's Formula?
Heron's formula to calculate the area of the triangle is:
A = √( s(s-a)(s-b)(s-c) )
Where "s" represents the semi-perimeter or half of the perimeter of the triangle and can be calculated as:
s = (a+b+c)/2
a, b, and c are the side lengths of the triangle.
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Example1: If the length of the sides of a triangle ABC are 4 in, 3 in, and 5 in. Calculate its area.
Solution:
To find: Area of the triangle ABC.
AB = 4 in, BC = 3 in, AC = 5 in(given)
Using Heron's Formula,
A = √( s(s-a)(s-b)(s-c) )
Finding s,
s = (a+b+c)/2
s = (4+3+5)/2
s = 6
Put the values,
A = √( 6(6-4)(6-3)(6-5) )
A = √( 6(2)(3)(1) )
A = √( 36) = 6
Answer: The area of the triangle is 6 in2.
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Example 2:
Area of an equilateral triangle is √3 squared unit. Find the length of the sides of the triangle.
Solution:
To find: The length of the sides of the triangle.
Area = √3(given)
Let the length of the triangle is "a" unit.
Using Heron's Formula,
A = √( s(s-a)(s-b)(s-c) )
Finding s,
s = (a+a+a)/2
s = (3a)/2
Put the values,
A = √( (3a/2)(3a/2-a)(3a/2-a)(3a/2-a) )
A = √( (3a/2)(a/2)(a/2)(a/2) )
A = (a/2)(a/2)√3
Putting the value of A,
√3 = (a/2)(a/2)√3
a = 2
Answer: The length of the sides of the equilateral triangle is 2 units.