Sir Mike Ambrose is the author of the question.
Let the single side length of the regular hexagon be 2 units.
Therefore;
Area regular pentagon is;
5(2.12920428618)²÷(4tan(180/5))
= 7.79980...
6²+6²-2*6*6cosa = 12²+3²+2*12*3cosa
72-72cosa = 153+72cosa
144cosa = 81
a = acos(9/16)
a = 55.7711336722°
b = 180-a
b = 124.2288663278°
6²+12²-2*6*12cosc = 6²+3²+2*6*3cosc
180-144cosc =...
tana = 5/11
a = atan(5/11)°
sin(atan(5/11)) = 5/b
b = 12.0830459736 cm.
c = b-2.5
c = 9.5830459736 cm.
sin(atan(5/11)) = d/9.5830459736
d = 3.9654926392 cm.
5/11 = 3.9654926392/e
e...
Let the side length of the ascribed square be 1 unit.
tanc = 0.5/1
c = atan(½)°
cos(atan(½)) = a/1
a = 0.894427191 units.
d² = 2(1²)
d= √(2) units.
d is the diagonal of the ascribed sq...
Let a be the radius of the circle.
b²+2² = a²
b = √(a²-4) units.
c = 5+2
c = 7 units.
d = 3a units.
It implies;
Calculating a.
(3a)² = √(a²-4)²+7²
9a² = a²-4+49
8a² = 45
a =...
tana = 3/4
a = atan(¾)°
a is angle ACB.
Let b be the radius of the three inscribed congruent circles.
c = (4-5b) units.
Calculating b.
tan(0.5atan(¾)) = b/(4-5b)
⅓ = b/(4-5b)
3b = 4...
Area of the ascribed regular Pentagon is;
5/(4tan(180/5))
= 1.72047740059 square units.
Single side length of the formed small inscribed regular Pentagon is;
Let it be x.
x² = (1/(1-co...
Calculating x.
Let AC = BD = 1 unit.
a = 180-30-40
a = 110°
a is angle CAD.
(1/sin30) = (b/sin110)
b = 1.8793852416 units.
b is CD.
c = 1+b
c = 2.8793852416 units.
c is BC.
d²...
Calculating x.
Let CD = 1 unit.
a = 180-70-30
a = 80°
(1/sin30) = (b/sin80)
b = 1.969615506 units.
c = 180-80-40
c = 60°
(1.969615506/sin60) = (d/sin80)
d = 2.2397641135 units....
Blue Area is;
Area square with side length 4 units - 3(area circle with radius 1 unit)
= (4*4)-3(1²*π)
= (16-3π) square units.
