Problem:
A regular octagon ABCDEFGH has sides of length two. Find the area of △ADG.
Answer Choices:
A. 4+22
B. 6+2
C. 4+32
D. 3+42
E. 8+2
Solution:
Construct the right triangle △AOB as shown in the figure. Since AB=2, we have AO=2 and AD=2+22. Similarly, we have OG=2+2, so
Area(△ADG)=21(2+22)(2+2)=(1+2)(2+2)=4+32.
Answer: C.
The problems on this page are the property of the MAA's American Mathematics Competitions
