I am to find the area of an equilateral triangle whose side is 5... I know I need to find the highth before I find the area, but I end up with a hight of the square root of 31.25, is this right? if so how do I continue and solve for the area with this kind of number?

Answer 1

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You can use Heron of Alexandria's formula

Area= sqrt(s(s-a)(s-b)(s-c))

where s is one half perimerter, and a,b,c are the sides of the triangle.

Area= sqrt(15/2 *(5/2*5/2*5/2))

area= sqrt((5/2)^4 (3))
= 25/4 sqrt 3 which is your answer.

Now your height. I get h=5sin60=5sqrt3/2= 4.33
area= 1/2 b*h= 1/2*5*4.33 which is the same as Heron's formula.

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