Mathematics Question and Solution
15² = a²+6²
a² = 225-36
a = √(189)
a = 3√(21) units.
b = 2a
b = 6√(21) units.
sin75 = c/b
c = 6√(21)sin74
c = 26.5585692881 units
d = 10+c
d = 36.5585692881 units.
cos75 = e/(6√(21))
e = 7.1163471929 units.
sinf = 6/15
f = 23.5781784782°
g = 75-f
g = 51.4218215218°
h = 180-2g
h = 77.1563569564°
j² = 2*15²-2*15²cos77.1563569564
j = 18.7074571083 units.
k = 15-½(j)
k = 5.6462714458 units.
l = k+5+j-e
l = 22.2373813613 units.
m = j-e
m = 18.7074571083-7.1163471929
m = 11.5911099154 units.
Area Orange is;
Area rectangle with width 22.2373813613 units and length 36.5585692881 units - Area triangle with height 26.5585692881 units and base 11.5911099154 units - Area sector with radius 15 units and angle 150° + Area triangle with radius 15 units and angle 150°
= (22.2373813613*36.5585692881)-(0.5*26.5585692881*11.5911099154)-((150π*15*15)/360)+(0.5*15*15sin150)
= 420.7708881019 square units.
= 420.77 square units to 2 decimal places.
