Question 1084696

A triangle with the length of {{{5cm}}} on each side is an equilateral triangle;

its perimeter is {{{P=5cm+5cm+5cm=15cm}}}

and its area is {{{A=(1/2)*5cm*h}}}

to find {{{h}}} use right angle triangle whose legs are {{{h}}} and {{{5cm/2=2.5cm}}} and hypotenuse is {{{5cm}}}

{{{(5cm)^2=(2.5cm)^2+h^2}}}

{{{25cm^2=6.25cm^2+h^2}}}

{{{25cm^2-6.25cm^2=h^2}}}

{{{18.75cm^2=h^2}}}

{{{h=sqrt(18.75cm^2)}}}

{{{h=4.330127018922193cm}}}

{{{A=(1/2)*5cm*4.330127018922193cm}}}

{{{A=10.82531754730548cm^2}}}

{{{A=10.83cm^2}}}