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
Altitude (triangle) Altitude (triangle) In geometry, an altitude of a triangle is a line segment through a vertex and perpendicular to (i.e., forming a right angle with) a line containing the base (the side opposite the vertex). This line containing the opposite side is called the "extended base" of the altitude. The intersection of the extended base and the altitude is called the "foot" of the altitude. The length of the altitude, often simply called "the altitude", is the distance between the extended base and the vertex. The process of drawing the altitude from the vertex to the foot is known as