Calculating radius of the circle.
Let x be the diameter of the circle.
a²+x² = (3+1)²
a = √(16-x²) units.
It implies;
√(16-x²) ~ ½(x)
(3+1) ~ 2√(3)
Cross Multiply.
2√(48-3x²) =...
Calculating Triangle ADE.
a² = (3√(3))²+(4√(3))².
a² = 27+48
a = √(75)
a = 5√(3) units.
a is AC.
3√(3)b+4√(3)b+5√(3)b = 3√...
Calculating Triangle ADE.
a² = (3√(3))²+(4√(3))².
a² = 27+48
a = √(75)
a = 5√(3) units.
a is AC.
3√(3)b+4√(3)b+5√(3)b = 3√(3)*4√(3...
Calculating ratio Red length to Blue length.
a² = 2(1)²
a = √(2) units.
a is the side length of the bigger square.
tanb = 1/(1+1)
b = atan(½)°
c = 45-b
c = (45-atan(½))°
tan(45-atan...
Calculating Area ABCD (square).
Notice.
The green triangle is an isosceles right-angled triangle.
Let the side length of the square be x.
Calculating x.
(x/sin45) = (a/sin(180-45-30))...
Calculating The Required Shaded Area.
Let it be x.
a² = 1²+0.5²
a = √(1.25) units.
b = 2a
b = 2√(1.25) units.
tanc = 1/0.5
c = atan(2)°
tan(atan(2)) = d/√(1.25)
2 = d/√(1.25)
d...
Calculating Length x.
a² = 2²+(2+1)²
a = √(13) units.
a is the each of the two adjacent lengths of the green isosceles right-angled triangle.
tanb = 3/2
b = atan(3/2)°
c = 45-atan(2/3)...
Calculating red area.
tana = 10/5
a = atan(2)°
b = 2a
b = 2atan(2)°
c = 180-b
c = 180-2atan(2)
c = 2atan(½)°
Area red is;
Area sector with radius 5 units and angle 2atan(2)°-Area...
Calculating Area Ascribed Regular Hexagon.
Let x be the side length of the ascribed regular hexagon.
a² = 2x²-2x²cos120
a = √(3)x units.
a is DF.
sin60 = b/x
b = ½√(3)x units.
sin30...
Calculating Angle FGM (angle alpha).
Let the single side length of the hexagon be 2 units.
Therefore;
AG =√(8-8cos150) units.
Calculating AH.
AH = √((8-8cos150)+4-4√(8-8cos150)cos105)...
