Mathematics Question and Solution
Calculating Shaded Green Area.
sin30 = a/2
a = 1 unit.
(a')²+1² = 2²
a' = √(4-1)
a' = √(3) units.
a'' = 2a'
a'' = 2√(3) units.
a'' is the side length of the inscribed regular triangle.
b² = 2²+2²-2*2*2cos30
b² = 8-8cos30
b = 1.03527618041 units.
c²+a² = b²
c² = 1.03527618041²-1²
c = 0.26794919243 units.
d = 2c
d = 2*0.26794919243
d = 0.53589838486 units.
Shaded Green Area is;
Area quarter circle with radius 2 units+Area equilateral triangle with side length 2√(3) units-3(area triangle with height 1 unit and base 0.53589838486)-6(area sector with radius 2 units and angle 30°)+6(area triangle with height 2 units and base 2sin30 units).
= ¼(π*2²)+½(2√(3))²sin60-3*½(0.53589838486*1)-6(30π*2²/360)+6(½*2²sin30)
= π+3√(3)-0.80384757729-6.28318530718+6
= π+3√(3)-1.08703288447
= 8.3377450763-1.08703288447
= 7.25071219183 square units.
= 7.25 square units to 2 decimal places.
