Verification of Areas Using Heron’s Formula
In this section, we explore the application of Heron’s formula, which enables the calculation of the area of a triangle given the lengths of its sides. The formula states that
\[
\text{Area} = \sqrt{s(s-a)(s-b)(s-c)}
\]
where \(s\) is the semi-perimeter defined as \(s = \frac{a + b + c}{2}\), with \(a\), \(b\), and \(c\) representing the sides of the triangle.
We begin with an example triangle park with sides measuring 40m, 32m, and 24m. Calculating the semi-perimeter gives \(s = 48m\) and using Heron's formula, we find the area matches our verification through the traditional base-height method, showcasing the consistency and effectiveness of the formula. We then apply Heron’s formula to additional triangles, examining an equilateral triangle with a side of 10 cm, and an isosceles triangle with sides measuring 5 cm and 8 cm, thus verifying versatility in various triangle types.
This section reinforces the significance of Heron’s formula in practical applications where traditional height-based area calculations may not be feasible.