Mathematics Question and Solution
Notice;
The diameter of the semicircle is 8 units.
Therefore radius is 4 units.
tan30 = a/2
a = ⅔(√(3)) units.
b = 3a
b = 2√(3) units.
c² = 2²+(⅔(√(3)))²
c = (4/√(3)) units.
d = (2/√(3))+c
d = 2√(3) units.
e² = 4²+4²-2*4*4cos120
e = 4√(3) units.
f = atan((4/√(3))/2)
f = atan(2/√(3)°
g² = 4²+4²-2*4*4cos(180-2atan(2/√(3)))
g = (8√(21)/7) units.
h = (atan(2/√(3))-30)°
Area Maroon exactly in square units is;
Area triangle with height (8√(21)/7) units and base 4√(3)sin(atan(2/√(3))-30) - Area triangle with height (2/√(3)) units and base 2√(3)sin60 units.
= 0.5*(8√(21)/7)*4√(3)sin(atan(2/√(3))-30)-0.5*(2/√(3))*2√(3)sin60
= (24√(3)/7)-√(3)
= ⅐(17√(3)) square units.
