An equilateral triangle and a regular hexagon have equal perimeters.
If the area of the equilateral triangle is x.
Find the area of the regular hexagon.
Ans.: 1.5x
請問各位可詳細解釋中間的步驟嗎?
THZ!>,<
求area of hexagon問題
2013-04-04 4:15 pm
回答 (2)
2013-04-04 4:51 pm
參考: 我
2013-04-04 6:13 pm
Let perimeter of the equilateral triangle be p, so one of the sides = p/3.
Area of the triangle = (1/2)(p/3)^2 sin 60 = (p^2 sqrt 3)/36 = x.
Since perimeter of the hexagon is also = p, so one of the side of the hexagon = p/6
Area of hexagon = 6 x area of equilateral triangle with side p/6
= 6 x (1/2)(p/6)^2 sin 60 = 6 x (p^2/36) (sqrt 3)/4 = (3/2)(p^2 sqrt 3)/36 = 1.5x.
Area of the triangle = (1/2)(p/3)^2 sin 60 = (p^2 sqrt 3)/36 = x.
Since perimeter of the hexagon is also = p, so one of the side of the hexagon = p/6
Area of hexagon = 6 x area of equilateral triangle with side p/6
= 6 x (1/2)(p/6)^2 sin 60 = 6 x (p^2/36) (sqrt 3)/4 = (3/2)(p^2 sqrt 3)/36 = 1.5x.
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