A small regular hexagon is inscribed in a circle. A large regular hexagon circumscribes the circle, as shown in the figure. If the area of the large regular hexagon is 10 square units, Find the are of the small hexagon.
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bubupin

2007-08-26 01:00
area of large hexagon : area of small hexagon
=2^2:(3^(1/2))^2=4:3
area of small hexagon=10*3/4=7.5

孫文先

2007-08-26 10:15
旋轉圓內的小正六邊形使它的頂點落在大正六邊形的中點上，如此不須計算，只要適當切割小正六邊形即可知大正六邊形與小正六邊形之面積比為4:3

bubupin

2007-08-26 22:36
孫老師的這個解答比較好