## Giant Clock, Bug Speed

The largest four-faced clock in the USA is the Allen Bradley Clock Tower in Milwaukee, Wisconsin. The diameter of its face is 40 feet 3.5 inches, and its minute hand is 20 feet in length. If you are a bug sitting on the very tip of the outer end of the minute hand, how fast are you traveling?

## Interior Segments of Square

A square has sides each having a length of 2. Segments are drawn from one vertex to the midpoints of each of the four sides of the square. What is the sum of the lengths of these segments?

## Circular Lawn with Path

A circular grass plot 12 feet in diameter is cut by a straight gravel path 3 feet wide, one edge of which passes through the center of the plot. The number of square feet in the remaining grassy area is:

1. 36 – 34
2. 30 – 15
3. 36 – 33
4. 35 – 9√3
5. 30 – 9√3

## Billy the Goat

Billy the goat is tied to the corner of Patty�s barn. The barn is 20 x 40 feet, and the rope is 50 feet long. No trees or other obstructions are in the way. What is the available area of grass that Billy can eat? (Draw a good picture of this area first.)

## Marvin and Deedee

A: Marvin tied his dog, Deedee, with a rope 10 meters long at an outside corner of his regular hexagonal walled garden having sides of 8 meters. What is the area of ground that Deedee can cover, as determined by the limits of the rope and the walls?

B: Now do the same problem with Deedee tied inside the garden.

## Split Parallelogram Area

PQRS is a parallelogram. Let m be a line that passes through the parallelogram in such a way that it splits the area into two equal parts. How many such lines can there be? If you were to draw all of these lines, you would notice something about them: What is it?