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 =...
Let AD be x.
a² = x²+4²-2*4*xcos30
a = √(x²+16-4√(3)x) units.
a is BD.
b² = x²+3²-2*3*xcos30
b = √(x²+9-3√(3)x) units.
b is CD.
c² = 4²+3²-2*3*4cos60
c² = 25-12
c = √(13) units.
c is BC.
Calcula...
Calculating R, radius of the circle.
a²+4² = 6²
a = √(36-16)
a = √(20)
a = 2√(5) units.
b²+4² = 10²
b = √(100-16)
b = √(84)
b = 2√(21) units.
Therefore;
2√(5)*2√(21) = 4c
c = √(1...
Let the two equal lengths be 1 unit each.
(1/sin20) = (a/sin40)
a = 1.87938524157 units.
b = a-1
b = 0.87938524157 units.
(1/sin20) = (c/sin(180-40-20))
c = 2.53208888624 units.
d² = 2(2.5320888...
Green Area is;
Area square with length 4 units - Area quarter circle with radius 2 units - Area square with length 2 units - 3(Area square with length 1 unit) - Area square with length 3 units +...
