Maria has drawn some shapes on identical square pieces of paper, as shown. Each line she has drawn is parallel to an edge of her paper. How many of her shapes have the same perimeter as the sheet of paper itself?
A. 1
B. 2
C. 3
D. 4
E. 5
D. 4
In the first, fourth, fifth and sixth diagrams, it is easy to see that the sides of the shapes that do not lie along the sides of the squares have a direct correspondence to the parts of the sides of the squares that are not part of the perimeter of the shapes. However, in the second and third diagrams, there are some extra sides to the shapes (highlighted in bold) that do not have such a correspondence. Hence the number of shapes with the same perimeter as the square piece of paper is four.
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