Question: Is there a method of finding the area of a trapezium or/and parallelogram even if the height is not given? Could you also explain how to find the height?

Thanks in advance

Shayne,

If all you know is the lengths of the sides then this is not enough information to calculate the area, even for a parallelogram The reason is that you can construct many different parallelogram with these side lengths and quite different areas. This is even true if all four sides are of the same lengths. Below are example I made with 4 tooth picks.

To find the area you need some other information such as the size of one of the angles or the length of a diagonal.

Penny