Question 921447
1. Here is the triangle ( {{{green(h)}}}= height in centimeters):
{{{drawing(300,300,-7,7,-2,12,
green(rectangle(0,0,-0.5,0.5)),
triangle(-6,0,6,0,0,10.4),
green(line(0,0,0,10.4)),
locate(-3,5.2,12),locate(0.1,5,green(h)),
locate(2.4,5.2,12),
locate(-3.5,0.7,6)locate(2.5,0.7,6)
)}}} {{{6^2+h^2=12^2}}} according to the Pythagorean theorem
{{{6^2+h^2=12^2}}} ---> {{{36+h^2=144}}} ---> {{{h^2=144-36}}} ---> {{{h^2=108}}} ---> {{{h=sqrt(108)}}} ---> {{{h=sqrt(36*3)}}} ---> {{{h=sqrt(36)*sqrt(3)}}} ---> {{{h=6sqrt(3)}}}
The area of a triangle is calculated as {{{area=(1/2)*base*height}}} , so for this triangle
{{{area=(1/2)*12*6sqrt(3)}}} ---> {{{highlight(area=36sqrt(3))}}} square centimeters.
 
2. Here is the triangle ( {{{x}}}= length of half of the base, in cm):
{{{drawing(420,300,-7,7,-1,9,
green(rectangle(0,0,-0.5,0.5)),
triangle(-6,0,6,0,0,8),
green(line(0,0,0,8)),
locate(-3,4,10),locate(0.1,2.5,8),
locate(2,4,10),
locate(-3.2,0.5,x)locate(2.8,0.5,x)
)}}} {{{x^2+8^2=10^2}}} according to the Pythagorean theorem
{{{x^2+8^2=10^2}}} ---> {{{x^2+64=100}}} ---> {{{x^2=36}}} ---> {{{x=sqrt(36)}}} ---> {{{x=6}}} ,
so the base of the triangle measures {{{2*6cm=12cm}}}
The area of a triangle is calculated as {{{area=(1/2)*base*height}}} , so for this triangle
{{{area=(1/2)*12*8}}} ---> {{{highlight(area=48)}}} square centimeters.