Just attempt to verify this: http://math.stackexchange.com/questions/115743/question-about-a-rotating-cube

RotatingCube.m

(* ::Package:: *)

heron[side1_,side2_,base_]:=Module[{p,s},( 
	p=(side1+side2+base)/2;
	s=Sqrt[p (p-side1)(p-side2)(p-base)])]


getHeight[side1_,side2_,base_]:=Module[{cos,sin,h},( 
	cos=(side1*side1+base*base-side2*side2)/(2*side1*base);
	sin=Sqrt[1-cos*cos];
	h=side1*sin)]


makeTwoSides[t_]:={Sqrt[1+t*t],Sqrt[1+(1-t)*(1-t)]}


curve=getHeight @@ (makeTwoSides[t]~Join~{Sqrt[3]})//
	Simplify[#,0<=t<=1]&


Plot[curve,{t,0,1}]