sin60 = 0.5d/a
a = ⅓√(3)d units.
a is the radius of the half circle.
Therefore, total blue area in terms of d is;
2(60π*⅓√(3)d*⅓√(3)d/360)+(0.5*⅓√(3)d*⅓√(3)dsin120)-(0.5*⅓√(3)d*⅓√(3)dsin60)...
a = ½(d) units.
a is the radius of the green half circle.
b = d+a
b = ½(3d) units.
c² = (½(3d))²-(½(d))²
c² = ¼(8d²)
c = √(2(d)²)
c = √(2)d units.
c is the diameter of the small blue se...
Notice!
Triangle ABM is equilateral.
Calculating a:b.
Let AB be 1 unit.
c = 90-60
c = 30°
cos30 = (0.5*1)/d
d = ½÷½√(3)
d = 1/√(3)
d = ⅓√(3) units.
d is the radius of the semi cir...
a = ⅓(90)
a = 30°
sin30 = b/4
b = 2 cm.
sin60 = c/4
c = 2√(3) cm.
d = √(4²-2²)-√(4²-(2√(3))²)
d = √(12)-√(4)
d = (2√(3)-2) cm.
d = 1.4641016151 units.
Area Blue is;
Area trapez...
Let a be 1 unit.
b = 1+(2*1)+1
b = 4 units.
c = ½(b)
c = 2 units.
2d² = 4²
d² = 8
d = 2√(2) units.
e² = 1²+(2√(2))²-2*2√(2)cos45
e = √(9-4)
e = √(5) units.
(√(5)/sin45) = (1/si...
Let the side length of the inscribed square be a.
Calculating the area of the inscribed red square.
2b² = a²
b = ½√(2)a unit.
c² = 2a²
c = √(2)a unit.
c is the diagonal of the inscribed...
Calculating area of the inscribed blue half circle.
a = ½(6+4)
a = 5 units.
a is the radius of the ascribed semi circle.
b = a-4
b = 1 unit.
c²+1² = d²
d = √(c²+1) units.
c is the rad...
Notice!
Triangle ABC is equilateral.
Let AB be 1 unit.
a = 180-42-12
a = 126°
a is angle BDC.
(1/sin126) = (b/sin42)
b = 0.8270909153 units.
b is CD.
c² = 1+0.8270909153²-2*0.827...
a² = 4²+1²
a = √(17) units.
b = a-1
b = (√(17)-1) units.
b = 3.1231056256 units.
c² = (√(17)-1)²+3²
c² = 17-2√(17)+1+9
c = √(27-2√(17)) units.
c = 4.3305644838 units.
tand = (√(17)-1...
a = 10+10
a = 20 cm.
a is twice the radius of the quarter circle.
b = ½(10)
b = 5 cm.
c² = 5²+10²
c √(125)
c = 5√(5) cm.
Observing similar plane shape (right-angled triangle) side len...
