Area Pink is;
¼(π*3²)-½(3²)+3((¼π)-½)
= ¼(9π)-½(9)+¼(3π)-½(3)
= ¼(12π)-½(12)
= 3π-6
= 3(π-2) square units.
Calculating x.
Notice.
AC = BC
Let a be alpha.
It implies;
sina = 0.5x/(1+4)
sina = ⅒(x) --- (1).
Again.
sina = 1/x --- (2).
Equating (1) and (2).
⅒(x) = 1/x
x² = 10
x...
Calculating the area of the ascribed half circle.
Let a be the radius of the circle.
b² = a²+(3√(3))²
b = √(a²+27) units.
c = ½(3+b)
c = ½(3+√(a²+27)) units.
d = c-3
d = ½(3+√(a²+27))-3
d = ½(√(...
Calculating red Area.
Notice.
3x = 4-x
4x = 4
x = 1 unit.
Where x is the radius of the red quarter circle and the inscribed white half circle.
y = 4-x
And x = 1 units.
y = 4-1
y = 3...
Calculating Length FE.
tana = 10/20
a = atan(½)°
b = 2a
b = 2atan(½)°
c = 180-2b
c = 180-4atan(½)
d² = 2(20)²-2(20)²cos(180-4atan(½))°
d = 24 units.
d is DE.
Notice.
DF = 20 units.
Therefore,...
Calculating Shaded Area.
a = 180-40-30
a =110°
a is angle BAC.
(6/sin40) = (b/sin30)
b = 4.66717148058 cm.
b is AB.
c = a-90
c = 20°
cos20 = (0.5*4.66717148058)/d
d = 2.4833500749...
Calculating Shaded Area.
Radius of the inscribed circle is 3 cm.
tana = 6/3
a = atan(2)°
b = a-45
b = (atan(2)-45)°
c = 90-a
c = atan(½)°
d = 180-2c
d = 180-2atan(½)
d = 2atan(2)°
e² = 2(3)²
e...
Let the side length of the square be a.
tanb = (0.5a)/a
b = atan(½)°
c = 90-b
c = atan(2)°
sin(atan(2)) = d/a
d = 0.894427191a units.
Calculating a.
(3√(2))² = (0.894427191a)²+a²-...
Calculating Length MA.
Let a be the AB, side length of the regular hexagon.
b = (a-3) units.
b is AM.
c = ½(a) units.
c is AK = FK.
Let d be CM = KM.
It implies;
d² = a²+3²-2*3acos120
d² = a²+9...
Calculating Area Triangle ABC.
Let a be the height of the triangle.
b = √(a²+4) units.
b is AC.
c = √(a²+9) units.
c is BC.
Calculating a.
½(2+3)a = ½√(a²+4)*√(a²+9)sin45
10a =...
