Question

Quadrilateral ABCD is a rhombus with diagonals that intersect at point E. Given angle ABE = 30 degrees and segment AD = 5, what is the area of triangle EBC?

Answer 1

it is a rhombus so ab=bc=cd=ad=5
and from the graph ABE=CBE=30degrees
so \[BE=5*\sin 30=5\sqrt{3}/2\]
\[CE=5*\cos 30=5/2\]
area ebc=\[0.5*(5\sqrt{3}/2)*(5/2)=25\sqrt{3}/8\]