1 maths problem

圖片參考：http://img832.imageshack.us/img832/5993/maths.png

Let BP = BS = DQ = DR = x ,then RS = PQ = 2x ,
AS^2 + AR^2 = RS^2(10 - x)^2 + (10 - x)^2 = (2x)^22(10 - x)^2 = 4x^2

(10 - x)^2 = 2x^2x^2 - 20x + 100 = 2x^2x^2 + 20x - 100 = 0x = { - 20 ± √[(20^2 - 4(1)(-100)] } / 2

x = 4.142... or x = - 24.142...(rejected)

Area of the Hexagon = Square ABCD - △SAR - △PCQ

= 10^2 - (1/2)(10 - x)^2 - (1/2)(10 - x)^2

= 100 - (10 - x)^2

= 100 - (10 - 4.142...)^2

= 65.685... = 65.7 cm²