Mathematics Question and Solution
Let the single side length of the regular dodecagon be be 1 unit.
Therefore;
Area purple is;
Area triangle with height √(3) unit and base 1 unit.
= ½*√(3)*1
= ½√(3) square unit.
Area ABCD (square) is;
Area square with side (1+√(3)) unit.
= (1+√(3))²
= 1+2√(3)+3
= 2(2+√(3)) square unit.
It implies;
Area Purple ÷ Area ABCD (square) in its simplest form is;
½√(3) ÷ 2(2+√(3))
= √(3) ÷ (8+4√(3))
= ¼(2√(3)-3)
