The area of a given triangle can be calculated in various ways depending on what is known about the triangle.
*** Area = half base multiplied by vertical height ***
Three cases must be considered: (a) the right triangle, (b) an acute triangle, (c) a scalene triangle. In all three cases, the same formula emerges
Area △ ABC = ½ base x vertical height = ½ b.h
*** Basic Points and the Pythagorean Theorem ***
The right-angled triangle (or simply a right triangle) has one right-angle - that is one 90o angle
In the next diagram, △ ABC has a right angle at vertex A. Since the three angles of a triangle add to 180o it follows that the angles at vertices B and C add to 90o
The HYPOTENUSE (BC) of the triangle is the longest side and is opposite the right-angle.
If an ALTITUDE is drawn from vertex A to the hypotenuse (at point D), then there are three similar triangles △ ABC ~ △ BAD ~ △ CAD
Taking the triangles in pairs enables us to write various ratios.