Equilateral triangle terms of side length "a" can be derived directly using the Pythagorean theorem or using trigonometry. The area of a triangle is half of one side "a" times the height "h" from that side: The legs of either right triangle formed by an altitude of the equilateral triangle are half of the base "a", and the hypotenuse is the side "a" of the equilateral triangle. The height of an equilateral triangle can be found using the Pythagorean theorem so that Substituting "h" into the area formula (1/2)"ah" gives the area formula for the equilateral triangle: Using trigonometry, the area of
Heronian triangle triangles with these sidelengths, and joins them together along the sides of length "a", to obtain a triangle with integer side lengths "c", "e", and "b" + "d", and with area If "a" is even then the area "A" is an integer. Less obviously, if "a" is odd then "A" is still an integer, as "b" and "d" must both be even, making "b"+"d" even too. Some Heronian triangles cannot be obtained by joining together two right-angled triangles with integer sides as described above. For example, a 5, 29, 30 Heronian triangle with area 72 cannot be constructed from two