Mathematics Question and Solution
Calculating yellow area.
a = 2+3
a = 5 units.
b²+3² = 5²
b² = 25-9
b = √(16)
b = 4 units.
c = 2+b+3
c = 9 units.
c is the length of the rectangle.
d ~ 3
3 ~ 9
Cross Multiply.
9d = 9
d = 1 units.
Let r be the radius of the biggest half circle.
2r = c+d
2r = 9+1
2r = 10
r = 5 units.
Again, r is the radius of the biggest half circle and also the width of the rectangle.
e²+3² = 5²
e = √(25-9)
e = 4 units.
tanf = 3/4
f = atan(3/4)°
g = 180-f
g = (180-atan(3/4))°
Therefore, yellow area is;
Area rectangle with length and width 9 units and 5 units respectively - Area triangle with height and base 4 units and 3 units respectively - Area sector with radius 5 units and angle (180-atan(3/4))°.
(9*5)-(½*4*3)-((180-atan(3/4))π*5²/360)
= 45-6-31.22614431
= 7.77385569 square units.
