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To find the perimeter and areas of complex shape without a grid you should divide the shape into simple shapes and find the area of each shape alone and then add up the areas all together to get the area of the whole shape. Example: If there is a shape that can be divided into 2 triangles and 1 rectangle then you will find the area of each triangle alone and then the area of the rectangle then add up all the areas together.
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Why would you need to separate a figure into parts to calculate perimeter and area?
You don't need to if you can manage to work out the perimeter and area of complex shapes. Most people cannot work easily with shapes other than triangles, quadrilaterals, circles and semicircles. For them (us) it is easier to partition the shape.
Can two shapes have the same perimeter?
Yes - even shapes with different area.
Can a shape have the same area but not perimeter?
Most shapes have different perimeter than area, as far as value.
What is the area and perimeter of a cylinder?
There is no perimeter of a circle. Only flat shapes have perimeters. You can however, find the circumference, surface area, and volume.
How shapes have the same area but different perimeter?
Because the area is different than the perimeters
