The formula to calculate the area of a triangle using Heron's Formula is:
\[ \text{Area} = \sqrt{s(s - a)(s - b)(s - c)} \]
Where:
Heron's Formula is a mathematical formula used to calculate the area of a triangle when only the lengths of its sides are known. It is important because it provides a simple and efficient way to find the area of any triangle, regardless of its shape or angles. By using Heron's Formula, we can avoid complex trigonometric calculations and rely solely on the lengths of the sides. This makes it a valuable tool in various fields, such as architecture, engineering, and surveying, where the area of triangles needs to be determined accurately and quickly.
Let's consider an example:
Using the formula to calculate the area of the triangle:
\[ s = \frac{5 + 6 + 7}{2} = 9 \]
\[ \text{Area} = \sqrt{9(9 - 5)(9 - 6)(9 - 7)} = \sqrt{9 \times 4 \times 3 \times 2} = \sqrt{216} \approx 14.70 \text{ square units} \]
This means that the area of the triangle for this scenario is approximately 14.70 square units.