Mathematics Question and Solution
Calculating area shaded.
tana = 2/4
a = atan(½)°
b = 180-2a
b = (180-2atan(½))°
c = 180-b
c = 180-(180-2atan(½))
c = 2atan(½)°
Notice.
Radius of the inscribed half circle r, is;
r = ½(4)
r = 2 units.
Area Shaded is;
Area triangle with height and base 4 units and 2 units respectively - Area triangle with height 2 units and base 2sin(180-2atan(½)) units - Area sector with radius 2 units and angle 2atan(½)°
= ½(2*4) - ½*2*2sin(180-2atan(½)) - (2atan(½)π*2*2/360)
= 4-1.6-1.854590436
= 0.545409564 square units
= 0.55 square units to 2 decimal places.
