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
Pythagoras Peak theorem concerning a right-angled triangle is well known. Pythagoras Peak Pythagoras Peak is the highest peak, 1,275 m, in the central Tula Mountains, standing along the north side of Beaver Glacier, 8 nautical miles (15 km) southeast of Mount Storer. The peak has a prominent notch, the eastern aspect being a right-angled triangle with a perpendicular northern face. It was photographed from Mount Riiser-Larsen in February 1958 by ANARE (Australian National Antarctic Research Expeditions) led by Phillip Law, but was first visited and surveyed in December 1958 by G.A. Knuckey, ANARE surveyor. It was named by the Antarctic Names Committee