The Heron's formula, also known as Hero's formula or Héron's formula, is a mathematical formula used to calculate the area of a triangle when the lengths of all three sides are known. This formula is named after the ancient Greek mathematician Heron of Alexandria, who first recorded this formula in his book "Metrica" in the 1st century AD.
Mathematically, the Heron's formula is expressed as follows:
Area = √(s(s-a)(s-b)(s-c))
Here, a, b, and c represent the lengths of the triangle's sides, and s is the semiperimeter of the triangle, defined as half the sum of the lengths of all sides, that is:
s = (a + b + c) / 2
The formula involves several key components. The side lengths of the triangle (a, b, and c) must be known accurately, and the semiperimeter s needs to be calculated. By using this formula, we can calculate the area of the triangle by multiplying the square root of the product of s with (s-a), (s-b), and (s-c). The square root (√) is used to obtain the final value in a suitable unit of the triangle's length.
The Heron's formula serves as a useful alternative when information about the triangle is insufficient to use the regular formula for the area of a triangle, which is half the product of the base length and the triangle's height. In certain cases, the Heron's formula is more efficient and minimizes the risk of errors when calculating the area of a triangle.
Mathematically, the Heron's formula is expressed as follows:
Area = √(s(s-a)(s-b)(s-c))
Here, a, b, and c represent the lengths of the triangle's sides, and s is the semiperimeter of the triangle, defined as half the sum of the lengths of all sides, that is:
s = (a + b + c) / 2
The formula involves several key components. The side lengths of the triangle (a, b, and c) must be known accurately, and the semiperimeter s needs to be calculated. By using this formula, we can calculate the area of the triangle by multiplying the square root of the product of s with (s-a), (s-b), and (s-c). The square root (√) is used to obtain the final value in a suitable unit of the triangle's length.
The Heron's formula serves as a useful alternative when information about the triangle is insufficient to use the regular formula for the area of a triangle, which is half the product of the base length and the triangle's height. In certain cases, the Heron's formula is more efficient and minimizes the risk of errors when calculating the area of a triangle.
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