Mathematics Question and Solution
Let DE be 1 unit.
AC = 4 units.
Area ABC is;
8sin60
= 4√(3) square units.
a² = 1+2²-4cos45
a = 1.47362575821 units.
(1.47362575821/sin45) = (1/sinb)
b = 28.6750500631°
c = 60-b
c = 31.3249499369°
d = 360--60-150
d = 150°
e = 240-d
e = 90°
f² = 1²+1²
f = √(2) units.
g = 180-15-45-60
g = 60°
h² = 4²+1.47362575821²-8*1.47362575821cos31.3249499369
h = 2.84622917461 units.
(2.84622917461/sin31.3249499369) = (1.47362575821/sini)
i = 15.61499741821°
j = 60-i
j = 44.38500258179°
k = 120-j
k = 75.61499741821°
l = 180-k
l = 104.38500258179°
m = 120-104.38500258179
m = 15.61499741821°
(√(2)/sin104.38500258179) = (n/sin15.61499741821)
n = 0.39298743895 unit.
Area Lilac is;
0.5 + (0.5√(2)*0.39298743895sin60)
= 0.5 + 0.24065467519
= 0.74065467519 square units.
It implies;
Area Lilac ÷ Area ABC to 2 decimal places is;
= 0.74065467519 ÷ (4√(3)
= 0.10690429402
≈ 0.11
