<p>Three vertices of a cube, no two of which lie on the same edge, are joined to form a triangle. If an edge of the cube has length 1, what is the area of the triangle?</p>
<p>(a) root(6)/2
(b) root(3)/2
(c) root(2)/2
(d) root(6)/4
(e) root(3)/4</p>
<p>I have the answer, please explain!</p>
<p>Before I give my explanation, is the answer B?</p>
<p>Yes, the answer is B. :)</p>
<p>Here’s how I did it. First draw a 3D picture on a piece of paper, then plot the three vertices that make up the triangle, but they can’t be on the same edge. Now that they are made you have to find each individual length. If you look at the one square that 1 of the lines is on, then label the the edges 1. Do Pythagorean theorem, so 1^2 +1^2=c^2. So 2=C^2, so C=rad(2). Do this for the other lines and you will see that they are all rad(2). This means that it is an equilateral triangle, so all angles are 60 degrees. Now draw an equilateral triangle separately. Draw an altitude to the base creating a 90 degree angle, which also bisects the 60 degree angle making it 30 degrees. Now if the base was rad(2) as we found out earlier, the half a base that we created will be rad(2)/2. All angles of a triangle add up to 180 so 90 + 30=120, so the last angle is 60 degrees. That’s a special triangle, so you take the half base and multiply it by rad(3) to get rad(6)/2. Now we plug into the area of a triangle formula. 1/2<em>the base which is rad(2)</em>height/altitude which is rad(6)/2, and you get rad(12)/4. Make the radical rad(4*3), then 2rad(3). Simplify the fraction by dividing the numerator and the denominator by 2 and you get rad(3)/2</p>
<p>Ahhh giatns beat me to it. Haha, any questions? :P</p>
<p>Yeah, sorry educationOD. Hope it helped :D</p>
<p>Thanks guys! 
Makes sense now! :)</p>
<p>Exactly how. I solved it haha</p>
<p>why do you multiply the half base (aka rad(2)/2) by rad(3)?</p>
<p>EDIT: NEVERMIND…IM A DUMB NUT xD</p>
<p>And just so I can redeem my self for that stupid post I made above, I came up with a faster way to get to the answer (although it’s built off of giatns). Once you get that the three sides are rad(2), just use K=0.5absinC=0.5<em>rad(2)</em>rad(2)*sin(pi/3)=rad(3)/2.</p>
<p>:D</p>