Geometry Challenges

1. Draw any triangle with point P on the triangle. Describe the construction of the line through P that divides the triangle into two equal areas.

2. Given 100 yards of fencing, consider what shapes could be enclosed and the areas of each.

3. For perimeter = 100, what triangular region has the maximum area? (Consider using a spreadsheet.)

4. How many triangles are there with perimeter 100 and integer area? (Another good one for using a spreadsheet.)

5. What fraction of the original area is the area of the triangle in the middle?


6. A barn sits in a field; it is 8 miles from point A and 5 miles from point C. How far is the barn from the nearest road which extends from A to C?



7. A farmer has two fields of the same size. The circles represent areas for crop growth due to irrigation. Which provides growth on a larger proportion of the field?