Area of Triangles
This tutorial is designed to explore the different formulas used to calculate the area of of triangles using an applet.
We first recall some of the most widely used formulas used to calculate the area of a triangle.
1 - When a base and the corresponding height are known, the area A of the triangle may be calculated as follows:
A = (1 / 2) * h * BA
2 - When two sides and the angle between them are known, the area A of the triangle may be calculated as follows:
A = (1 / 2) * CB * CA * sin (C)
3 - When all three sides of a triangle are known, the area A of a triangle may be calculated using Heron's formula:
A = sqrt [ s * (s - BC) * (s - CA) * (s - AC) ]
where s in the above formula is given by s = (1 / 2)(AB + BC + CA)
Interactive Tutorial
1 - Press the button above to start the applet and maximize the window obtained.
2 - A triangle with vertices A, B and C and the values of all its three sides and internal angles (in degrees) are displayed. You can DRAG any vertex of the triangle to change its sides and angles.
3 - Drag any of the vertices, write down the values of h, the three sides and angles and use all three formulas shown above to check that you get close answers (this is due to rounding errors).
4 - For Heron's formula, you may want to use the calculator in this website.
More geometry references
Geometry Tutorials, Problems and Interactive Applets.
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