Question

Let abcdef be a regular hexagon.What is the ratio of area of triangle ace to area of hexagon abcdef

Answer 1

Answer:

Area of ΔACE : area of hexagon :: 1 :2

Step-by-step explanation:

Let abcdef be a regular hexagon.What is the ratio of area of triangle ace to area of hexagon abcdef

Let say Hexagon side = a

area of hexagon = (3√3 / 2)a²

Regualr hexa gon has internal angle = 120°

AC² = AB² + BC² - 2AB BC Cos120

=> AC² = a² + a² - 2a²(-1/2)

=> AC² = a² + a² + a²

=> AC = 3a²

=> AC = √3a

Similarly AE = CE = AC = √3a

Area of ΔACE

= (√3 / 4) (√3a)²

= (3√3 / 4)a²

Area of ΔACE  / area of hexagon = (3√3 / 4)a²/(3√3 / 2)a² = 2/4 = 1/2

Area of ΔACE : area of hexagon :: 1 :2