Express the area of an equilateral triangle as a function of the length of a side.
thanks for your help
2007-05-23 19:24:14 · 6 answers · asked by Mr. Rain 1 in Science & Mathematics ➔ Mathematics
Equilateral Triangle
s = length of a side
(s^2 * sqrt3)/4
["s" squared, times the square root of 3, all divided by 4]
2007-05-23 19:29:49 · answer #1 · answered by deepseaofblankets 5 · 0⤊ 0⤋
Drop an altitude from the vertex. Splits base (x) in half. Left half is a right triangle. Base of it is half the base of the equilateral triangle, x/2. Hypotenuse (whole base of triangle is x). So altitude h is
h² = x² - (x/2)²
h² = x² - x²/4
h = (x/2)â3
So area is (x/2)(x/2)â3 = (x²â3)/4
2007-05-24 02:32:55 · answer #2 · answered by Philo 7 · 0⤊ 0⤋
area=a root 3/4
2007-05-24 02:34:41 · answer #3 · answered by aditi.merchant 1 · 0⤊ 0⤋
Let the side be x
so the height h= (x/2)*tan60
h = (sqrt(3))/2*x
area of the triangle: (1/2)*side*height
A=(1/2)*x*(sqrt(3))/2*x
A=(sqrt(3))/4*sqr(x)
2007-05-24 02:41:18 · answer #4 · answered by andekhianjaani 1 · 0⤊ 0⤋
area = 1/2 x (Length^2)
2007-05-24 02:29:48 · answer #5 · answered by kolo 1 · 0⤊ 2⤋
Let a side be a.
Area = [sqrt(3)/4] * a^2
2007-05-24 02:30:55 · answer #6 · answered by Jain 4 · 1⤊ 0⤋