Question

please solve this question because today is my exam

Answer 1

this can be easily done by showing the traingles congruent

Answer 2

As quad PSDA is a parallelogram
PS = AD ...opp sides are equal.
Now PQ = QR = RS.
PQ = 1/3 PS
similarly
AB = BC = CD.
CD=1/3 AD
But
PS = DA.
Thus,
PQ = CD.
As PS is parallel to AD
Thus.
Angle QPE = Angle FDC
As they are interior alternate angles.
Now,
PQB= CBQ. Alternate interior angles.
But
CBQ = DCF corresponding angles.
Thus,
PQB = DCF.
Now,
In triangles PQE & CFD.
PQB = DCF.
PQ = CD.
QPE = FDC
Thus,
Triangle PQE = Triangle CFD are congruent by angle-side-angle test.
Thus Area of PQE = Area of CFD as both the triangles are congruent.