Standard Four – Middle Level Problems
Prompt: A garden is fenced in the shape of a regular hexagon with each side 1- meters
in length. A dog is tied with a 12-meter leash to one of the posts on the outside of the
garden. What area can the dog cover?
Answer: 97 1/3 pi square meters
Mathematics Teacher December 1995 V88 N9
Prompt: Suppose that you have a square piece of paper on which you draw the largest
possible circle. You cut out the circle and discard the leftover scraps of paper. Inside
the circle you draw the largest possible square, cut it out, and discard the leftover
scraps of paper. How much of the area of the original square remains?
Answer: ½
Mathematics Teacher December 1995 V88 N9
Prompt: Determine the area of the quadrilateral with given lengths and a right angle at A.
The University of Northern Colorado, Math Contest, November 1994
Prompt: The sum of the lengths of the three sides of a right triangle is 90 inches. The
sum of the squares of the lengths of the three sides is 3362 square inches. Determine
the area of the triangle.
Grassl and Mingus. "Problem Solving: Exploring paths less Travled." 2005: 77-99.
Prompt: To swim a mile in a certain rectangular swimming pool, one must either swim
the long length 80 times or negotiate the perimeter of the pool 22 times. What is the
total number of square yards in the area of the pool?
Grassl and Mingus. "Problem Solving: Exploring paths less Travled." 2005: 77-99