SOLUTION: The vertices of a cube of side length 2cm are connected to form a triangle as shown. What is the area of the triangle? Image- https://media.discordapp.net/attachments/8027514148

Algebra ->  Triangles -> SOLUTION: The vertices of a cube of side length 2cm are connected to form a triangle as shown. What is the area of the triangle? Image- https://media.discordapp.net/attachments/8027514148      Log On


   

Question 1175874: The vertices of a cube of side length 2cm are connected to form a triangle as shown. What is the area of the triangle?
Image- https://media.discordapp.net/attachments/802751414874537995/814628051726893166/AAAAAElFTkSuQmCC.png
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

here you have equaterial triangle and side length is equal to the diagonal of a cube
if a cube of side length 2cm, diagonal is
d=sqrt%28%282cm%29%5E2%2B%282cm%29%5E2%29
d=sqrt%284cm%5E2%2B4cm%5E2%29
d=sqrt%282%2A4%29cm
d=2sqrt%282%29cm
=> equal to the side a of a equaterial triangle
a=2sqrt%282%29cm
we need height of a triangle
h=sqrt%28a%5E2-%28a%2F2%29%5E2%29
h=sqrt%28%282sqrt%282%29%29%5E2-%282sqrt%282%29%2F2%29%5E2%29
h=sqrt%288-%288%2F4%29%29
h=sqrt%288-2%29
h=sqrt%286%29
the area of the triangle:
A=ah%2F2
A=%28sqrt%288%29%2Asqrt%286%29%29%2F2
A=2+sqrt%283%29cm%5E2->exact solution
A=3.46cm%5E2