Geometry: An Interactive Journey to Mastery

Lesson 22: Explorations with Pi

 A dog is tied to the corner of two buildings

with a leash that is 13 yards long, as shown in

)LJXUHͼ௘$OOPHDVXUHPHQWVDUHLQ\DUGV௘ͽ

The dog is convinced that a bone is buried

somewhere in the yard, but its movement, of

course, is restricted by the length of the leash. Find

the total area of ground the dog can reach from its

leash.

 Two rectangles and two sectors are arranged as shown

in )LJXUH.

Each rectangle is 2 inches by 8 inches. What is the sum of the

areas of the two sectors?

 )LJXUH shows two concentric circles and a line segment of

length 7 tangent to the small circle.

If the radius of the small circle is 6, what is

D௘ͽ WKHUDGLXVRIWKHODUJHFLUFOH"

E௘ͽ WKHDUHDEHWZHHQWKHWZRFLUFOHV"

 A sector is inscribed in a regular heptagon. The sides of the sector

match the sides of the heptagon. What, to one decimal place, is the

DUHDRIWKHVKDGHGUHJLRQVKRZQLIWKHVLGHOHQJWKRIWKH¿JXUHLV

LQFKHV"ͼ௘6HH)LJXUH௘ͽ

10

10

4

6

8

13

Figure 22.11

60°

Figure 22.12

7

Figure 22.13

Figure 22.14