The side lengths of a quadrilateral are not sufficient to define the figure. The area cannot be figured with this information alone.

If you have other information about the quadrilateral, then the area can be computed. You might know, for example, that there is one right angle, that two sides are parallel, that the diagonals cross at right angles, or the length of a diagonal. Any of these bits of additional information is sufficient to finish the definition of the figure.

Consider sticks in relative lengths of 9, 15, 28, and 40. Consider how you might arrange them in a quadrilateral. You will quickly find that there are multiple ways to do it--each having a different area.

If you have other information about the quadrilateral, then the area can be computed. You might know, for example, that there is one right angle, that two sides are parallel, that the diagonals cross at right angles, or the length of a diagonal. Any of these bits of additional information is sufficient to finish the definition of the figure.

Consider sticks in relative lengths of 9, 15, 28, and 40. Consider how you might arrange them in a quadrilateral. You will quickly find that there are multiple ways to do it--each having a different area.