Mathematics Question and Solution
tana = 12/8
a = atan(3/2)°
b = 180-a
b = (180-atan(3/2))°
(10/sin(180-atan(3/2))) = (4/sinc)
c = 19.4400348282°
d = 180-b-c
d = 180-19.4400348282-(180-atan(3/2))
d = 36.8698976458°
e = 90-d
e = 90-36.8698976458
e = 53.1301023542°
It implies, Area S (shaded area green) is;
Area trapezoid with height 12 units, and parallel sides 4 units and 12 units respectively - Area triangle with height 10 units and base 4sin36.8698976458 units - Area sector with radius 10 units and angle 53.1301023542°
= ½(4+12)*12 - ½*10*4sin36.8698976458 - (53.1301023542π*10²/360)
= (16*6) - 12 - 46.3647609001
= 96-12-46.3647609001
= 84-46.3647609001
= 37.6352390999 square units exactly in decimal.
= 37.64 square units to 2 decimal places.
