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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.
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Solution
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
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