Mathematics Question and Solution
Calculating Ratio Purple Area and Orange Area.
Let 2 be the radius of the inscribed orange area.
It implies;
Area orange inscribed circle is;
π(2)²
= 4π square units.
tan30 = 2/a
a = 2√(3) units.
b = 2a
b = 4√(3) units.
b is the side length of the inscribed regular triangle.
sin30 = 2/c
c = 4 units.
c is the radius of the ascribed circle.
Calculating area purple.
⅓((½*(4√(3))²sin60)-π(2)²)+(120π*4²/360)-(½*4²sin120)
= ⅓(12√(3)-4π)+⅓(16π)-(4√(3))
= 4√(3)-⅓(4π)+⅓(16π)-4√(3)
= ⅓(16π)-⅓(4π)
= ⅓(12π)
= 4π square units.
It implies;
Purple Area Ratio Orange Area is ;
Purple Area : Orange Area
= 4π:4π
= 1/1
= 1
