Question

The given figure shows a rectangle ABDC and a parallelogram ABEF; drawn on opposite sides of AB.
Prove that: 
(i) Quadrilateral CDEF is a parallelogram;
(ii) Area of the quad. CDEF
= Area of rect. ABDC + Area of // gm. ABEF.

Answer 1

After drawing the opposite sides of AB, we get

Since from the figure, we get CD//FE, therefore, FC must parallel to DE. Therefore it is proved that the quadrilateral CDEF is a parallelogram.

The area of the parallelogram on the same base and between the same parallel lines is always equal and the area of the parallelogram is equal to the area of a rectangle on the same base and of the same altitude i.e, between the same parallel lines. 

So Area of CDEF= Area of ABDC + Area of ABEF 
Hence Proved