Problem solving typically involves using algebra to set up an equation or system of equations which must be solved to find the possible solutions. The simplest might be to find the value of
given the sides of a polygon in terms oftogether with a value for the perimeter.
Example: The perimeter
of the trapezium below is found by adding up the lengths of all the sides:
Suppose we know that
We havein terms of
so we can equate 99 and
to obtain the equation
and we solve this equation to obtain
Suppose we are told instead that the area is 66. The formula for the area of a trapezium is
so given the expressions for the lengths of the sides on the diagram above we can find the area in terms of
We equate 66 and
We solve this equation:
or 
Only
is possible since
means negative values for the lengths.