the perimeter of an equilateral triangle is 3s. In the terms of s, what is the area of the equilateral trian?

Question

can u plese tell me how u did the work plz?

thank you!!!

Answer 1

triangle has 3 sides and the perimeter is 3s
so.. divide 3s by 3 and you get s
s is the length of one side of the triangle
so.. in order to find the area of the triangle, you need the formula base x height x 1/2
in order to find the height you need to use the Pythagorean theorem

(1/2s)^2+h^2 = s^2
h^2 = s^2-1/4s^2
h=sqrt(3/4s^2)

base = s
height = sqrt(3/4s^2)

[s*sqrt(3/4s^2)]/2 = the area of the triangle.

Answer 2

the area formula for an equilateral triangle is:
A = sqrt(3)/4 * side^2

the perimeter is 3s. Divide by 3 to get the sides, which is s

A = sqrt(3)/4 * s^2

Answer 3

since the perimeter=3s
each side=s ( being equilateral triangle)
so perpendicular height h=sq rt{s^2-(1/2 s)^2}= sq rt{s^2-(1/4)s^2}=sq rt{(3/4) s^2}
or h=s/2 sq rt (3)
so the area of triangle= 1/2 x base x height
or =1/2 x s x s/2 sq rt(3)
=(1/4) s^3 sq rt(3) ans

Answer 4

The area is
1/2(s x scos30)=1/2sxs cos30
or
1/2sxssin 60