Let the radius of the red inscribed circle be r.
Calculating r.
2a² = 6²
a = √(18)
a = 3√(2) units.
2b² = 8²
b = √(32)
b = 4√(2) units.
c² = 6²+8²
c = √(36+64)
c = 10 units.
10²...
Calculating yellow area.
2² = 2a²-2a²cos120
Where a = regular hexagon side length.
120° = single interior angle of the regular hexagon.
It implies;
4 = 3a²
a = (2/√(3)) units.
a = 1.1547005384 u...
Calculating r, radius of the quarter circle.
a = (r-2) units.
Therefore;
r² = b²+(r-2)²
r²-(r²-4r+4) = b²
b² = 4r-4
b = √(4r-4) units.
c = (r-4) units.
Therefore;
r² = d²+(r-4)²
r²-(r²-8r+16) = d²...
Notice, the ascribed quadrilateral is regular (square).
Calculating Area Blue.
a² = 4²+8²
a = √(16+64)
a = √(80)
a = 4√(5) units.
b = ½(a)
b = ½(4√(5))
b = 2√(5) units.
tanc = 4/8
c...
Let the two equal lengths be 1 unit.
a = 100-60-20
a = 100°
(b/sin20) = (1/sin100)
b = 0.3472963553 units.
c = 360-120+100
c = 360+220
c = 140°
It implies;
d² = 1+0.3472963553²-2*0.3472963553co...
Calculating Orange Area.
Notice, radius of the three congruent circles is 2 units each.
Orange Area is;
Area semi circle with radius 2 units + Area equilateral triangle with side 2 units + 2(area...
Calculating angle x.
Let the base of the quadrilateral be 1 unit.
a = 180-64+86
a = 30°
(1/sin86) = (b/sin64)
b = 0.9009888098 units.
(c/sin30) = (1/sin86)
c = 0.501220949 units.
d = 180-8-84
d...
Calculating angle x.
Let the two equal lengths of the ascribed square be 1 unit.
tan10 = 1/a
a = 5.6712818196 units.
a is the square side considering the assume 1 unit.
b = a-1-1
b = 5.6712818196...
Calculating r, radius of the two congruent circles.
It implies;
(2r)² = (2+r)²+1-2(2+r)cos60
4r² = 4+4r+r²+1-2-r
3r² = 3+3r
r²-r-1 = 0
Resolving the above quadratic equation via completing the sq...
Calculating area red.
a = 4+6 = 10 units.
a is the side length of the two congruent regular composite plane shape.
b = ½(10)
b = 5 units.
c = 5-1
c = 4 units.
tans = 4/6
d = atan(2/3)°
e² = 6²+...
