Mathematics Question and Solution
Calculating radius of the largest half circle and area yellow.
a = 2+3
a = 5 units.
b²+3² = 5²
b = √(16)
b = 4 units.
c = 2+b+3
c = 2+4+3
c = 9 units.
Where c is the length or base of the rectangle.
d = ½(c)
d = 4.5 units.
Calculating r, radius of the largest half circle.
4.5²+3² = r²
r = = √(29.25)
r = ½(3√(13)) units.
r = 5.4083269132 units.
Calculating Area Yellow.
tane = 3/4.5
e = atan(3/4.5)
e = 33.690067526°
f = 180-e
f = 146.309932474°
Area Yellow is;
Area rectangle with length 9 units and width 5.4083269132 units - Area triangle with height 3 units and base 4.5 units - Area sector with radius 5.4083269132 units and angle 146.309932474°
(9*5.4083269132)-½(4.5*3)-(146.309932474π*4.5²÷360)
= 48.6749422188-6.75-37.3462544819
= 4.5786877369 square units.
