Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating a.
½((0, 6√(3)) (-3, 3√(3)) (a, (16a/3)) (0, 6√(3))) = ¼(9+20√(3))
Therefore;
a = x = ½√(3) unit
y = 16a/3 = (16/3)(√(3)/2)
y = ⅓(8√(3)) unit.
Therefore;
Area green is;
Area triangle with height (√(697-72√(3))/2√(3)) unit and base 6sin(120-atan(16√(3)/(36-3√(3))) unit
= ½*(√(697-72√(3))/2√(3))*6sin(120-atan(16√(3)/(36-3√(3)))
= ½(√(2091-216√(3)))sin(120-atan(16√(3)/(36-3√(3)))
= ½√(2091-216√(3)sin(120-atan((64√(3)+16)/141) square units.
= 20.2666604984 square units exactly in decimal.
