There are lots of reasons for leaves varying in shape and size, listed are just a few.
Water Retension: Plants living in dry condition are likely to have leaves with a small surface area that are often needle shaped in order to retain water. 90% of the water absorbed by a plant is lost through evaporation through the leaves.
Catching Food: Some plants have leaves shaped like slides, these are also slipperl and insects unfortunate enough to land on them are likely to slip into a vat of water and digestive juices.
Protection: Some plants have needle shaped leaves for protection from predators, a good example are the coniferous trees in the arctic. Their leaves are shaped like spines to deter hungry animals. There's not much sunlight or rain in the arctic so every leaf is precious.
Getting rid of excess water: Plants breath through tiny spores in their leaves, if these were to become clogged with water, the plant would effectively drown. Most leaves are shaped especially to allow water to run off them, with the veins in the leaves acting as gutters.
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curved straight random
pattern of shapes which leaves no room left over
If they are the same shapes but differ only in size, then they are SIMILAR shapes. Otherwise, they are simply different shapes.
Yes - even shapes with different area.
Yes many different shapes can have the same volume