What is the area of an equilateral triangle of side length 20 cm?

1 Answer
Nov 26, 2015

Answer:

#100sqrt(3)#

Explanation:

Referring to this image,
http://areeweb.polito.it/didattica/polymath/htmlS/argoment/ParoleMate/Gen_08/Img/TriangoloEquilatero%20(11)png
we know that #AB=AC=BC=20#.

This means that the height cuts #AB# in two equals parts, #AH# and #HB#, each #10# units long.

This means that, for example, #AHC# is a right triangle with #AC=20# and #AH=10#, so

#CH = sqrt(AC^2-AH^2) = sqrt(20^2-10^2)=sqrt(300)=10sqrt(3)#

Since we know the base and the height, then the area is

#(20*10sqrt(3))/2 = 100sqrt(3)#