Area of a Triangle — by Heron’s Formula
In this section, we explore how to calculate the area of a triangle using Heron's formula, especially useful when the height is not known. For a triangle with side lengths a, b, and c, the area can be calculated using the formula:
$$ Area = \sqrt{s(s-a)(s-b)(s-c)} $$
where \( s \) represents the semi-perimeter of the triangle given by \( s = \frac{a + b + c}{2} \).
Heron, an ancient mathematician, developed this method around 10 AD. The text presents practical examples, such as determining the area of a triangular park and other triangle types, including equilateral and isosceles triangles. The section culminates in various exercises to reinforce the learned concepts.