Area of regular polygon

是有工式的

nt^2/[4tan(180/n)]
= (8)(6)^2/[4tan(180/8)]
= 173.82 cm^2

但如果忘記了工式也可以畫圖計出來：

because it is regular...


圖片參考：http://imgcld.yimg.com/8/n/HA00799693/o/701204110064613873392220.jpg

area = 4 triangles + 4 rectangles + 1 square

triangle (yellow):
a^2 + a^2 = 6^2
2a^2 = 36
a = 4.243 cm
area of triangle = a x a / 2 = 4.243 x 4.243 / 2 = 9.00cm

rectangle (pink):
area = 6 x a = 6 x 4.243 = 25.456 cm

square (green):
area = 6 x 6 = 36cm

4 triangle + 4 rectangle + 1 square
= 4(9) + 4(25.456) + 36
= 173.82 cm^2

正多邊形其實係有面積公式的。
n:number of sides
t:side length:
nt^2
---------------=Area
4tan(180/n)
代返入d數字:
(8)(6)^2 / 4tan(180/8)
=72 / tan 22.5
=173.8233765....
=174 cm^2 (corr.to 3 sig .fig.)//