Mathematics Question and Solution
Sir Mike Ambrose is the author of the question.
Calculating Area Orange, exactly in square cm.
Let AB be x.
Therefore BC = 2x cm.
Calculating x.
Yellow area + Area triangle with height 2x cm and base ½(3x)sin60 cm = Area trapezoid with two parallel side ½(3x) cm and 2x cm, and height ½(3√(3)x) cm.
Therefore;
30√(3)+¾*√(3)x² = (21√(3)x²)/8
30+¾x² = (21x²/8)
240+6x² = 21x²
15x² = 240
Therefore;
x = 4 cm.
Calculating Area Orange, exactly in square cm decimal form.
It is;
Area trapezoid with two parallel side 4 cm and 6 cm, and height 6√(3) cm - Area triangle with height 6 cm and base 2.56973739837sin111.05172444 cm
= ½*6√(3)(4+6) - ½(6*2.56973739837sin111.05172444)
= 30√(3) - 7.19467258546
= 44.7668516416 cm²
