An equilateral triangle with a height of 20 has a base of 23.1 (23.09401), not 15. If the base is 15 then the height will be 13 (12.99038).
It is: 0.5*base*perpendicular height
Area = 1/2*base*perpendicular height.
The base length is 5.2643 units and the height is 4.55902 units.
The base is one third of the perimeter, half of the base times the height is the area.
Base times height and divided by 2.
You find the height by using Pythagoras' theorem and then 0.5*base*height = area.
The area of a triangle is one-half the product of the triangle's base and height. The height of an equilateral triangle is the distance from one vertex along the perpendicular bisector line of the opposite side. This line divides the equilateral triangle into two right triangles, each with a hypotenuse of 9c and a base of (9/2)c. From the Pythagorean theorem, the height must be the square root of {(9c)2 - [(9/2)c]}, and this height is the same as that of the equilateral triangle.
8.7
Area = 1443.376 cm2
0.5 x base length x vertical height
-- The area of any triangle is 1/2 (length of the base x height). -- For an equilateral triangle, that's equivalent to 1/2 x sqrt(3) x (length of a side).
The height of an equilateral triangle is √3/2 x side_length. So for an equilateral triangle of side length 2a, the area is: area = 1/2 x base x height 1/2 x (2a) x (√3/2 x 2a) = √3 a2