Just do what you would normally but don't add sticks
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For a regular diamond shaped kite, the area would be one half the product of the length of the two sticks. So if it was 20 inches and 30 inches the area would be 300 inches square.
A triangle only has three sides. If you put three sticks together, you can make a triangle. If you had four sticks, you cannot make a triangle. That is why only three sticks are needed.
Yes - the tail adds stability. Without it - the kite would just spin. The tail makes the bottom of the kite slightly heavier so it flies vertically.
It can be a kite.
Yes, all quadrilaterals will tessellate.