Mathematics Question and Solution
Calculating Total Inscribed Shaded Area.
Let x be the radius of the five congruent inscribed shaded circle.
a = (14.9-2x) cm.
b = 2x cm.
Calculating x.
(2x)² = x²+(14.9-2x)²
4x² = x²+222.01-59.6x+4x²
x²-59.6x+222.01 = 0
Therefore;
x ≠ 55.6076
x = 3.99244
x ≈ 4 cm.
c = 6x
c = 24 cm.
c is the length of the ascribed rectangle.
Total Shaded Area is;
3(area equilateral triangle with side 8 cm)+3(area circle with radius 4 cm)+½(area circle with radius 4cm)
= 3(½*8*8sin60)+3(π*4*4)+½(π*4*4)
= 48√(3)+48π+8π
= 48√(3)+56π
= 8(6√(3)+7π) cm²
= 259.067627364 cm²
Or
Total Shaded Area is;
5(area circle with radius 4 cm)+3(area equilateral triangle with side 8 cm)-9(area sector with radius 4 cm and angle 60°)
5(π*4*4)+3(½*8*8sin60)-9(60π*4*4/360)
= 80π+48√(3)-24π
= 56π+48√(3)
= 8(7π+6√(3)) cm²
= 259.067627364 cm²
