Discussion
Identify the correct statement.
Answer: D
The correct statement is that the shape of a figure determines the perimeter.
Perimeter depends on the shape and size of a figure, so different shapes made from the same pieces can have different perimeters. Twelve unit squares arranged as a 3 by 4 rectangle have perimeter 14 units, but in a 2 by 6 rectangle the perimeter is 16 units, though the area is 12 square units in both.
That same example disproves the first statement: equal areas do not mean equal perimeters. Conversely a 1 by 5 and a 3 by 3 rectangle both have perimeter 12 but areas 5 and 9, so equal perimeters do not mean equal areas. And the units differ: perimeter is a length (cm), area a square measure (cm2).
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