Construct a square with exactly one-fourth the area of your original square. How do you know that the new square has one-fourth the area of the original square?
b.
Construct a square with exactly one half the area of your original square. How do you know that the new square has one half the area of the original square?
c.
Construct a square with exactly three-fourths the area of your original square.
Think about how you might construct the exact side lengths needed for these squares. For example, the first square will need a side length exactly one half the original. The third square is very difficult! Close Tip
Problem C7
Recall that the centroid is the center of mass of a geometric figure. How could you construct the centroid of a square?
When you noticed concurrencies in the folds, were you sure that the segments were concurrent? What would convince you that, for example, the medians of every triangle really are concurrent?
