How to Calculate Quadrilateral Area

A quadrilateral is a four-sided polygon. Each one has four sides, four angles and two diagonals. The area of a quadrilateral is calculated by dividing it into triangles and summing. The challenge is finding the height of the triangles.

Difficulty: Moderate

Instructions

1. Calculate area by taking the area of two triangles. You can take this shortcut only if two sides of your quadrilateral are parallel. Multiply the average of the lengths (parallel sides) by the distance between them (perpendicular).

2. Work through an example. If the two perpendicular sides of the quadrilateral are 10 and 12, respectively, and the distance between them is 8, the area is:
   
   11 * ((10 + 12) / 2) * 8 = 88.

3. Calculate the area if the sides are not perpendicular. The easiest way to find the area of a quadrilateral is to divide it into two triangles. However, if this is not possible, the formula is:
   
   Area = Square root of [(s - a)(s - b)(s - c)(s - d) - 1/4(ac + bd + pg)(ac + bd - pq)]
   
   Where a, b, c and d are the four sides of the quadrilateral. P and q are diagonals, and s = (a + b + c + d) / 2.

4. Define the variables. Let's say you want to find the area for a quadrilateral with sides equal to 30, 31, 22, 28, 34 and 43, for sides a, b, c, d and diagonals p and q, respectively.

5. Work through an example. If we substitute the variables in the formula with our example variables, the formula is:
   
   [(55.5 - 30)(55.5 - 31)(55.5 - 22)(55.5 - 28) - 1/4(30 * 22 + 31 * 28 + 34 * 43)(30 * 22 + 31 * 28 - 34 * 43)]^1/2 = 725

References

• Math.com: Quadrilaterals