Question

In the given figure, AF//BE and PQ//RS, FC and ED are perpendiculars to RS. The area of parallelogram ABEF is equal to:

पर्याय

• rect. CDEF

• quad. CBEF

• 2 × ΔАCF

• 2 × ΔEBD

Answer 1

rect. CDEF

Explanation:

• Parallelogram ABEF has its base on the line RS (with length equal to segment AB) and lies between the parallel lines PQ and RS.
• Rectangle CDEF has its base on the line RS (with length equal to segment CD) and lies between the same parallel lines PQ and RS, where FC and ED are perpendiculars to RS.
• Since right-angled triangles ΔAFC and ΔBDE are congruent (as AF = BE, and FC = ED are parallel heights between the same parallels), translating triangle ΔAFC to the position of ΔBDE shows that the area of parallelogram ABEF is equal to the area of rectangle CDEF.