Mathematics Question and Solution
a = ½(12) cm.
a = 6 cm.
b = ⅙*180(6-2)
b = 120°
b is the single interior angle of the regular hexagon.
c² = 6²+12²-2*6*12cos120
c = 15.8745078664 cm.
c = 6√(7) cm.
c = 15.8745078664 cm.
c is the radius of the sector.
(15.8745078664/sin120) = (6/sind)
d = 19.1066053509°
e = 90+d
e = 109.1066053509°
e is the angle of the sector.
Therefore, shaded area exactly in decimal is;
Area sector with radius 6√(7) cm and angle 109.1066053509 - Area triangle with height 12 cm and base 6sin120 cm.
= (109.1066053509π*(6√(7))²/360)-(0.5*12*6sin120)
= 239.9379568803-31.1769145362
= 208.7610423437 cm²
Calculating shaded area exactly in cm²
sin30 = f/12
f = 6 cm.
g = ½(f)
g = 3 cm.
h²+3² = 6²
h = √(36-9)
h = √(27)
h = 3√(3) cm.
j = 12+g
j = 15 cm.
tank = 15/(3√(3))
k = atan(⅓(5√(3)))°
l = 90-k
l = atan(⅕(√(3)))°
m = 90+l
m = (90+atan(⅕(√(3))))°
Therefore, shaded area exactly in cm² is;
((90+atan(⅕(√(3))))π*(6√(7))²/360)-(0.5*12*6sin120)
= (7(90+atan(⅕(√(3))))π/10)-(18√(3))
= ((630+7atan(⅕(√(3))))π-180√(3))/10 cm²
