Find the area of the parallelogram ABCD. Support your answer with a proper reason.

Question

□ABCD is a parallelogram where \(\overline{AB}\) || \(\overline{CD}\) . E is a point on \(\overline{CD}\) If the area of ΔABE = 14.2 cm² , find the area of the parallelogram ABCD. Support your answer with a proper reason.

Answer 1

Area of ΔABE from figure = 14.2 cm

From theorem. 

Area of ΔADE + area of ΔBCE – area of ΔAEB 

∴ Area of ΔADE = area of ΔBCE, 

x + x = area of ΔAEB

2x = 14.2 cm 

x = 14.2/2  = 7.1 cm 

∴ Area of ΔADE = area of ΔBEC