Mathematics Question and Solution
Notice, radius of the three congruent circles is 7 cm each.
sin60 = a/14
a = 7√(3) cm.
a = 12.124355653 cm.
b = a+7+7
b = (7√(3)+14) cm.
b = 26.124355653 cm.
b is the length of the rectangle.
tan30 = c/7
c = ⅓(7√(3)) cm.
c = 4.0414518843 cm.
d = 7+7+2c
d = (14+⅓(14√(3)) cm.
d = 22.0829037687 cm.
d is the width of the rectangle.
tane = ⅓(7√(3))/7
e = atan(⅓√(3))°
e = 30°
cosf = ⅓(7√(3))/7
f = acos(⅓√(3))°
f = 54.7356103172°
g = 90-e
g = 90-atan(⅓√(3))
g = atan(√(3))
g = 60°
h = 180-60-54.7356103172
h = 65.2643896828°
7² = 4.0414518843²+j²
j = 5.7154760665 cm.
k = 7-j
k = 7-5.7154760665
k = 1.2845239335 cm.
l = 65.2643896828+30
l = 35.2643896828°
Therefore, area orange is;
Area rectangle with width 19.124355653 cm and length 22.0829037687 cm - Area sector with radius 7 cm and angle 120° - Area circle with radius 7 cm - 2(area sector with radius 7 cm and angle 65.2643896828°) - 2(area triangle with height 7 cm and base 4.0414518843sin54.7356103172 cm) + Area rectangle with length 14 cm and width 7 cm - Area semi circle with radius 7 cm + 2(area trapezoid with parallel sides 7 cm and 1.2845239335 cm respectively, and height 4.0414518843 cm) - 2(Area sector with radius 7 cm and angle 35.2643896828°)
= (19.124355653*22.0829037687) - (120*7²π/360) - 7²π - 2(65.2643896828π*7²/360) - 2(0.5*7*4.0414518843sin54.7356103172) + (7*14) - 0.5*7²π + 2(0.5(7+1.2845239335)*4.0414518843) - 2(35.2643896828π*7*7/360)
= 162.510897365 cm²
