Geometry: An Interactive Journey to Mastery



Solutions

6. $GHFDJRQKDVVLGHV2QHDFKVLGHRIWKH¿JXUHGUDZDWULDQJOH
   with apex at the center of the decagon, as shown in Figure S.21.7.

With the labels given, we see that tan x (^1) a, giving a (^) tan^1 x.
Now, 2x is 101 of a full turn, so 2 x 36010 36.
Thus, x = 18°, a (^) tan 18° 1 , and
area = 10 u˜˜^1122 aa (^1010) tan 18 |30.8.

7. D௘ͽ 6HHFigure S.21.8.
   The triangle on the left is half an equilateral triangle
   ͼ௘WKHPLUURUKDOILVEHORZLW௘ͽ
   Thus, h = 1. Using Example 1 from the lesson for
   WKHDUHDRIDSDUDOOHORJUDPZHKDYHDUHD î 
   E௘ͽ 6HHFigure S.21.9.
   hh   ^22  DQG DUHD    ˜^12
   F௘ͽ ^2 + 35^2 = 37^2 :HKDYHDULJKWWULDQJOH௘6HHFigure S.21.10௘ͽ
   Area =^12 ˜u 12 35 210.
   G௘ͽ 6HHFigure S.21.11.
   Area =    u˜˜^12


8. D௘ͽ 6HHFigure S.21.12.
   x^2 + x^2 = 7^2 , so x 72.
   Thus, area =   ˜˜ 22.

a

(^11)
x
Figure S.21.7

30°

(^22)

4

4

h

Figure S.21.8

10 10

8

h

Figure S.21.9

(^1235)
37
Figure S.21.10
Figure S.21.11

4

4

3

3

55

5

5

x

x

7

Figure S.21.12