About Heron's Formula
Heron of Alexandria was the first to give the formula. It's used to calculate the area of various triangles, including equilateral, isosceles, and scalene triangles, as well as quadrilaterals. When the sides of a triangle are known, we may apply Heron's formula to calculate the area. The area of the triangle is calculated using Heron's formula with the triangle's semi-perimeter and side lengths.
What do you mean by Heron's Formula?
Heron's formula is used to calculate the area of triangles and quadrilaterals when the lengths of all their sides are known. Hero's formula is another name for it. This formula for calculating the area of a triangle is independent of the triangle's angles. It is totally determined by the lengths of all triangle sides. It bears the letter "s," which stands for semi-perimeter, which is obtained by halves a triangle's perimeter. Similarly, the principle of determining the area is extended to determine the area of quadrilaterals.
Heron's Formula Definition
According to Heron's formula, the area of any triangle with lengths a, b, c, a perimeter of the triangle, P, and a semi-perimeter of the triangle as 's' is calculated using the following formula: Area of triangle ABC = √[s(s-a)(s-b)(s-c)]
- Here, s = Perimeter/2 = (a + b + c)/2
Solved example of Heron's Formula
Example: Determine the area of a triangle with lengths of 5 units, 6 units, and 9 units.
Sol:
- As we know that, a = 5 units, b = 6 units and c = 9 units
- Hence, Semi-perimeter, s = (a + b + c)/2 = (5 + 6 + 9)/2 = 10 units
- Area of triangle = √(s(s-a)(s-b)(s-c)) = √(10(10-5)(10-6)(10-9))
- ⇒ Area of triangle = √(10 × 5 × 4 × 1) = √200 = 14.142 unit2
- ∴ Area of triangle is 14.142 unit2???????
Maths Formulas prepared by HT experts are listed on the main page.
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