Mathematics Question and Solution
a = 4+8
a = 12 cm.
a is the radius of the quarter circle.
tanb = 12/4
b = atan(3)°
c = (60+atan(3))°
(12/sin(60+atan(3))) = (4/sind)
d = 14.4420678686°
e = 180-60-atan(3)-d
e = 120-atan(3)-14.4420678686
e = 33.9928809543°
f = 90-e
f = 90-33.9928809543
f = 56.0071190457°
(12/sin(60+atan(3))) = (g/sin33.9928809543)
g = 8.9669238624 cm.
h² = 4²+12²
h = √(16+144)
h = √(160)
h = 4√(10) cm.
Therefore;
Area Blue is;
Area triangle with height 4√(10) cm and base 8.9669238624sin60 cm + Area sector with radius 12 cm and angle 56.0071190457° - Area triangle with height 12 cm and base 12sin56.0071190457
= (0.5*4√(10)*8.9669238624sin60) + (56.0071190457π*12*12/360) - (0.5*12*12sin56.0071190457)
= 49.1138647087 + 70.3806214971 - 59.6957073346
= 119.4944862058-59.6957073346
= 59.7987788712 cm²
≈ 59.80 cm² to 2 decimal places.
