Detailed Summary
Heron's formula provides a method to calculate the area of a triangle when the height is not known. The formula states:
\[ A = \sqrt{s(s-a)(s-b)(s-c)} \]
where \(s\) is the semi-perimeter defined as:
\[ s = \frac{a + b + c}{2} \]
This section begins with a scenario of finding the area of a triangular park with known sides (40 m, 32 m, 24 m), highlighting the inadequacy of using height for area calculation.
It further discusses the historical context, noting the contributions of Heron of Alexandria who formulated this equation between 10 C.E. β 75 C.E.
Three examples demonstrate calculating the area using Heron's formula, validating results through methods such as the right triangle area calculation, and verifying through multiple triangle types (equilateral and isosceles). Exercises at the end reinforce learning by encouraging students to apply this formula to both given and constructed problems.