First note that P_1=ABCDE and P_2=A'B'C'D'E' are congruent pentagons, then the transformarion that we use to send P_1 to P_2 must preserve distances, which means that we only can use translatons, rotations and reflections. We first use the <u>translation</u> that sents C to C' to send P_1 to a pentagon P_3 that only shares shares the vertex C' with P_2, let D'' be the image of the vertex D under the translation, the distances of the segments CD, C'D' and C'D'' are the same. Therefore, we might use a <u>rotation</u> that sends C'D'' to C'D', this rotation to sends the pentagon P_3 to a pentagon P_4 that shares the side C'D' with P_2 and that its coungruent to both P_1=ABCDE and P_2=A'B'C'D'E'. Finaly, we might <u>reflect</u> P_4 across the line that goes trhough C'D' and so P_4 wil be send to P_2=A'B'C'D'E'.
The smaller rectangle is taking up space among the larger one. So in order to find the area of this shaded region, you need to subtract that smaller one from the larger one.
