MATH 113: Area of a Quadrilateral

This worksheet combines a geometric exploration of irregular quadrilaterals with practice in estimating and calculating area.
  1. Use a ruler to draw an irregular convex quadrilateral on a sheet of stiff paper.
  2. Cut out the quadrilateral.
  3. Estimate the area of the quadrilateral. It may help to calculate the area of the sheet of paper you started with.


  4. For each edge of the quadrilateral, use your ruler to mark the midpoint of the edge. Check your work by gently folding the corners of the quadrilateral together -- if you were to crease the paper along that fold, the crease should go through the mark.
  5. Use your ruler to connect the marks on the edges into a convex polygon. This polygon should have some special properties; what are they? (Is it a rectangle? a trapezoid?)


  6. Cut out the convex polygon you just drew. Compare its area to the area of the corner pieces from the original polygon. What do you find?



  7. Using your ruler, find the area of the cut out polygon.





  8. Use your answers to the previous two questions to calculate the area of your original quadrilateral.


  9. Are your estimates in 3 and 8 close? If not, what might have gone wrong?