ABCD is a trapezium with AD and BC parallel sides. The ratio of the area of ABCD to that of ΔAED is

$$\eqalign{ & {\text{Let EN }} \bot \,{\text{AD}} \cr & {\text{Area of }}\Delta {\text{AED}} = \frac{1}{2} \times {\text{EN}} \times {\text{AD}} \cr & {\text{Area of trapezium ABCD}} \cr & = \frac{1}{2}\left( {{\text{AD}} + {\text{BC}}} \right) \times {\text{EN}} \cr & \frac{{{\text{ar}}\left( {{\text{ABCD}}} \right)}}{{{\text{ar}}\left( {{\text{AED}}} \right)}} \cr & = \frac{{\frac{1}{2}\left( {{\text{AD}} + {\text{BC}}} \right) \times {\text{EN}}}}{{\frac{1}{2} \times {\text{EN}} \times {\text{AD}}}} \cr & = \frac{{{\text{AD}} + {\text{BC}}}}{{{\text{AD}}}} \cr} $$