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?
