Mathematics Question and Solution
Calculating The Required Shaded Area.
a = ¼(2R)
a = ¼(6)
a = 1.5 units.
b² = 2(3)²
b = 3√(2) units.
c² = 1.5²+3²-2*3*1.5cos150
c = ½(3√(7)) units.
c = 4.36396936676 units.
d² = (3√(2))²+1.5²-2*1.5*3√(2)cos45
d = ½(3√(5)) units.
d = 3.35410196625 units.
3² = 3.35410196625²+4.36396936676²-2*4.36396936676*3.35410196625cose
29.2743964674cose = 21.294228634
e = acos(21.294228634/29.2743964674)
e = 43.331039462°
Required Shaded Area is;
(0.5*4.36396936676*3.35410196625sin43.331039462)+(60π*3²/360)+(0.5*3²sin60)
= 5.02211431703+4.71238898038-3.89711431703
= 5.83738898038 square units.
