Question 221444
Find the area of an equilateral triangle in which each side has a length of 2cm.


Step 1.  Area of equilateral triangle is {{{A=bh/2}}} where b is the base and h is the height.  Draw a perpendicular line from one angle to the midpoint of the opposite side.  Doing this forms a right triangle and bisected in half the opposite side.


Step 2.  The base is 1/2 the side of the equilateral triangle or 2cm/2=1 cm.


Step 3.  The height can be calculated using the Pythagorean Theorem which states that the sum of the squares of the legs of a right triangle (h and b) is equal to the hypotenuse squared or side s=2 cm.


Then, {{{s^2=h^2+b^2}}}


{{{2^2=h^2+1^2}}}


{{{4=h^2+1}}}


{{{h^2=3}}}


{{{h=sqrt(3)}}}


Step 4.  ANSWER:  Area {{{A=bh/2=1*sqrt(3)/2=sqrt(3)/2}}} square centimeters.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J