Mathematics Question and Solution
Calculating Area Red.
tana = 5/10
a = atan(½)°
b = 2a
b = 2atan(½)°
c = b-45
c = 8.1301023542°
d² =10²+10²-2*10*10cos8.1301023542
d = 1.4177804018 units.
e = ½(180-8.1301023542)
e = 85.9349488229°
f² = 2*5²
f = 5√(2) units.
g = 10-f
g = 2.9289321881 units.
tanh = 10/5
h = atan(2)°
j = 2h
j = 2atan(2)°
k = j-90
k = 36.8698976458°
It implies, area red is;
Area triangle with height 1.4177804018 units and base 2.9289321881sin85.9349488229 units + Area sector with radius 10 units and angle 8.1301023542° - Area triangle with height 10 units and base 10sin8.1301023542 units + Area sector with radius 5 units and angle 36.8698976458° - Area triangle with height 5 units and base 5sin36.8698976458 units.
= (0.5*1.4177804018*2.9289321881sin85.9349488229)+(8.1301023542π*100/360)-(0.5*100sin8.1301023542)+(36.8698976458π*25/360)+(0.5*25sin36.8698976458)
= 2.0710678118+7.0948527302-7.0710678119+8.0437638599-7.5
= 2.63861659 square units.
≈ 2.64 square units to 2 decimal places.
