AB=24/4=6(cm),
设〈ABC=x度,x+2x+2x=180度,x=36度,
以C为圆心,AC长为半径画弧,并AB于E,
则△ECA∽△CBA,
设AC=x,
x/6=(6-x)/x,
x=3√5-3,
AC=3√5-3(cm),
BD/2=√(AB^2-AC^2/4)=(3/2)√(10+2√5),
BD=3√(10+2√5)(cm),
S菱形ABCD=AC*BD/2=(3√5-3)*3√(10+2√5)/2
=9√(10-2√5)(cm)..
AB=24/4=6(cm),
设〈ABC=x度,x+2x+2x=180度,x=36度,
以C为圆心,AC长为半径画弧,并AB于E,
则△ECA∽△CBA,
设AC=x,
x/6=(6-x)/x,
x=3√5-3,
AC=3√5-3(cm),
BD/2=√(AB^2-AC^2/4)=(3/2)√(10+2√5),
BD=3√(10+2√5)(cm),
S菱形ABCD=AC*BD/2=(3√5-3)*3√(10+2√5)/2
=9√(10-2√5)(cm)..