Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Let the square side be x unit.
Calculating x.
x² = (x-4)² + ((x/2)+√((x²/4)-16)²
320 = 32x
x = 10 units.
Therefore;
Shaded Area is;
Area triangle with height 8 units and base 4 units - Area sector with radius 10 units and angle 2asin(√(5)/5) + Area triangle with height 10 units and base 10sin(2asin(√(5)/5)) units.
= ½*8*4 - (2asin(√(5)/5)*10*10*π÷360) + ½*10*10sin(2asin(√(5)/5))
= 16 - 46.36476090008 + 40
= 56 - 46.36476090008
= 9.63523909992 square units.
= 56 - (2asin(√(5)/5)*10*10*π÷360) square units.
= (504 - 5πasin(√(5)/5))/9 square units.
