Question

The given figure shows a rectangle ABDC
and a parallelogram ABEF drawn on opposite sides of AB, prove that :
1. quadrilateral CDEF is a parallelogram and
2. area of quadrilateral CDEF is equal to area of rectangle ABDC + area of parallelogram ABEF

Answer 1

attachment have the solution

Answer 2

Area of EFCD = Area of ABCD + Area of AEFB

Step-by-step explanation:

Compare Δ ADE & ΔBCF

DE = CE   (opposite sides of parallelogram EFCD)

AD = BC  (opposite sides of parallelogram ABCD)

AE = BF    (opposite sides of parallelogram AFEB)

=> Δ ADE ≅ ΔBCF

=> Area of Δ ADE = Area of ΔBCF

Area of  EFCD = Area of ABCD + Area of AEFB  -  Area of Δ ADE + Area of ΔBCF

=> Area of EFCD = Area of ABCD + Area of AEFB

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