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
Special right triangle Ancient Egypt; that their surveyors did use ropes for measurement; that Plutarch recorded in "Isis and Osiris" (around 100 AD) that the Egyptians admired the 3 : 4 : 5 triangle; and that the Berlin Papyrus 6619 from the Middle Kingdom of Egypt (before 1700 BC) stated that "the area of a square of 100 is equal to that of two smaller squares. The side of one is ½ + ¼ the side of the other." The historian of mathematics Roger L. Cooke observes that "It is hard to imagine anyone being interested in such conditions without knowing the Pythagorean