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Start with a rectangle, which is a special type of a parallelogram. Suppose its height is A units and length is B units. Then its area is A*B sq units and its perimeter is 2*(A+B) units.
Now slide the top side horizontally, keeping the vertical height between the top and the bottom the same. The area will not change but the perimeter will increase because the sides have now become slanted and longer.
The rather griim figures below may help illustrate (the . are for spacing):
+------+.....+------+
|........|........\........\
+------+..........+------+
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Can a parallelogram and a rectangle have the same perimeters but different areas?
Yes.
What shapes have the same perimeter but different areas?
Most shapes can have the same area and different perimeters. For example the right size square and circle will have the same are but they will have different perimeters. You can draw an infinite number of triangles with the same area but different perimeters. This is before we think about all the other shapes out there.
Can shapes of the same area have different perimeters?
MOst of it
How shapes have the same area but different perimeter?
Because the area is different than the perimeters
Why can you have a shape with different perimeters but the same area?
they are different because perimeter is the out side of the shape and area is inside of the shape.
