SUMMARY
The area of a triangle can be calculated using its three heights (altitudes) with the formula A^{-1} = 4 √(H(H-h_a^{-1})(H-h_b^{-1})(H-h_c^{-1})), where H is the semi-sum of the reciprocals of the altitudes. Given the heights ha = 3 m, hb = 4 m, and hc = 5 m, the area computes to approximately 10.04 m². The online tool TrianCal can be utilized for visualizing and verifying the calculations. Heron's formula is not applicable in this context as it requires side lengths rather than altitudes.
PREREQUISITES
- Understanding of triangle geometry and properties
- Familiarity with altitudes and their relationship to triangle area
- Basic knowledge of mathematical formulas and calculations
- Experience using online calculators for geometric computations
NEXT STEPS
- Research the derivation and application of the area formula using triangle altitudes
- Explore the use of TrianCal for geometric visualizations and calculations
- Study Heron's formula and its limitations regarding triangle dimensions
- Learn about other methods for calculating triangle area based on different parameters
USEFUL FOR
Mathematicians, geometry enthusiasts, educators, and students seeking to deepen their understanding of triangle area calculations using altitudes.