To calculate the area of a scalene triangle (A):
\[ A = \sqrt{s \cdot (s - a) \cdot (s - b) \cdot (s - c)} \]
Where:
A scalene triangle is a type of triangle that has all sides of different lengths. This means that none of the sides are equal in length, making it distinct from other types of triangles such as equilateral, where all sides are equal, and isosceles, where two sides are equal. In addition to having unequal sides, a scalene triangle also has unequal angles.
Let's assume the following values:
Using the formula:
\[ s = \frac{5 + 6 + 7}{2} = 9 \]
\[ A = \sqrt{9 \cdot (9 - 5) \cdot (9 - 6) \cdot (9 - 7)} = \sqrt{9 \cdot 4 \cdot 3 \cdot 2} = \sqrt{216} \approx 14.70 \text{ square units} \]
The area of the scalene triangle is approximately 14.70 square units.
Let's assume the following values:
Using the formula:
\[ s = \frac{8 + 10 + 12}{2} = 15 \]
\[ A = \sqrt{15 \cdot (15 - 8) \cdot (15 - 10) \cdot (15 - 12)} = \sqrt{15 \cdot 7 \cdot 5 \cdot 3} = \sqrt{1575} \approx 39.68 \text{ square units} \]
The area of the scalene triangle is approximately 39.68 square units.