Geometry: An Interactive Journey to Mastery



E௘ͽ 6HHFigure S.21.13.

h^ 75 53andarea 253.^

F௘ͽ :HKDYHKDOIDQHTXLODWHUDOWULDQJOH

௘6HHFigure S.21.14௘ͽ

Thus, the side opposite the angle of 30° is 10,

and the Pythagorean theorem gives the remaining

side as 10 3.

We have area = 50 3.

G௘ͽ 6HHFigure S.21.15.

Area = u˜^12 rr r^2

H௘ͽ 7KHGLDJRQDORIWKHUHFWDQJOHGRHVSDVVWKURXJKWKHFHQWHU

of the circle. Because of the inscribed/central angle theorem,

ZHKDYHDQDUFRIƒ௘6HHFigure S.21.16௘ͽ

x  u    VR DUHD   ^

9. D௘ͽ %RWKWULDQJOHVKDYHWKHVDPHKHLJKW
   Because M is the midpoint of AB, they have the same
   base lengths, too. Thus, they have equal areas.
   E௘ͽ (DFKWULDQJOHKDVEDVHDQGDUHD
   So,^1210 ˜ H 25 gives height h = 5.


10. :HKDYHFRQJUXHQWWULDQJOHV௘6HHFigure S.21.17௘ͽ
    The shaded 8 of them have area 20. Thus, the full 12 of them
    ͼ௘KDOIDJDLQPRUH௘ͽPDNHVDUHD

Figure S.21.13

(^10) h 10
5 5
(^20) 10 3
10

30°

Figure S.21.14

r

r r

r

Figure S.21.15

x

180°

5

5

8

Figure S.21.16

A

BC

D

F E

Figure S.21.17