【答案】
分析:將圓內接正四邊形和圓內接正六邊形的邊長用圓的半徑表示出來,再求出圓內接正四邊形與正六邊形的面積表達式(用圓的半徑表示),然后即可得出其面積比.
解答:
解:設圓的半徑為r.如圖:
在正方形ABCD中,作邊心距OF,
則OF=OBsin45°=

r,
則AD=2×

r=

r,
圓內接正四邊形的面積為S
ABCD=(

r)
2=2r
2;
在正六邊形ABCDEF中,
AB=BO=OA=r,
則S
ABCDEF=6×

OA•OBsin60°,
=6×

r•rsin60°,
=6×

r
2,
=

r
2,
S
ABCD:S
ABCDEF=2r
2:

r
2=4:3

.
點評:此題主要考查正多邊形的計算問題,屬于常規(guī)題.解答時要熟悉正方形和正六邊形的面積計算方法,尤其要懂得分割計算再求和.