Mathematics Question and Solution
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the regular hexagon.
b = a-90
b = 30°
tan30 = 6/c
c = 6/(1/√(3))
c = 6√(3) cm.
Therefore, area orange is;
½*6*c
= ½*6*6√(3)
= 18√(3) cm²
Calculation purple area.
d² = 12²+12²-2*12*12cos120
d = 12√(3) cm.
e = d+c
e = 12√(3)+6√(3)
e = 18√(3) cm.
sin30 = f/e
f = ½*18√(3)
f = 9√(3) cm.
cos30 = g/e
g = ½√(3)*18√(3)
g = 9*3
g = 27 cm²
sin30 = h/(12√(3))
h = 6√(3) cm.
Area purple is
Area triangle with height 27 cm and width 9√(3) cm - Area with height 6√(3) cm and base 12 cm.
= ½*27*9√(3)-½*12*6√(3)
= ½(243√(3)-72√(3))
= ½(171√(3)) cm²
Therefore;
Area Orange ÷ Area Purple exactly is;
18√(3) ÷ ½(171√(3))
= 36/171
= 4/19
