### MATH 113: Area of a Quadrilateral

This worksheet combines a geometric exploration of irregular quadrilaterals with practice in estimating and calculating area.

- Use a ruler to draw an irregular convex quadrilateral on a sheet of stiff paper.
- Cut out the quadrilateral.
- Estimate the area of the quadrilateral. It may help to calculate the area of the sheet of paper you started with.

- 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.
- 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?)

- 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?

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

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

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