Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Green ÷ Area Rectangle.
Area rectangle is;
9x8 = 72 square units.
Area green is;
Area trapezoid with two parallel lengths (5+2-¾) units and height 5 units - Area sector of radius 5 units and angle (tan–¹(4/3))°.
= ½(7-¾)*5 - (tan–¹(4/3)*25π÷360)
= (125/8) - (5πtan–¹(4/3)/72)
= (1125-5πtan–¹(4/3))/72
= (7875 - 110tan–¹(4/3))/504 square units.
= 4.02914432746 square units.
Therefore;
Area Green ÷ Area Rectangle is;
= ((7875 - 110tan–¹(4/3))/504) ÷ 72
= (7875 - 110tan–¹(4/3))/36288
= 0.05596033788
