Area R is;
Area sector with radius 8 cm and angle 20.16632290743° - Area triangle with height 8 cm and base (4.2sin 20.16632290743) cm
= ( 20.16632290743 *64π÷360) - (½*8*4.2sin 20.166322907...
Let BC = 1 unit.
(1/sin36) = (a/sin72)
a = 1.6180339887 units.
a is BD = CD.
b = 180-12-30
b = 138°
b is angle BAD.
(1.6180339887/sin138) = (c/sin30)
c = 1.2090569265 units.
c is AB....
Area coloured is;
Area sector with radius 3 units and angle 120° - Area triangle with height 3 units and base 3sin120 units + Area triangle with height 3 units and base 3sin60
= (120*9π÷360) - (½*...
Let the congruent two inscribed semi circles radius be r.
a = (3-2r) units.
b = 2r units.
It implies, calculating r.
2²+a² = b²
2²+(3-2r)² = (2r)²
4+9-12r+4r² = 4r²
12r = 13
r = (13...
a = 36+18
a = 54°
Let one of the green triangle area side be b.
cos54 = c/b
c = bcos54 units.
c = 0.5877852523b units.
sin54 = d/b
d = bsin54 units.
d = 0.8090169944b units.
e = c+...
sin36 = c/b
c = bsin36 units.
c = 0.5877852523b units.
Calculating b.
b² = (0.5877852523b)²+(0.5(b+1))²
0.6545084972b² = ¼(b²+2b+1)
1.6180339888b²-2b-1 = 0
It implies;
b = 1.61803 unit...
Let the side length of the regular hexagon be 1 unit.
a² = 2-2cos120
a = √(3) units.
Area regular hexagon is;
2(½*sin120)+(1*√(3))
= ½√(3)+√(3)
= ½(3√(3)) square units.
= 2.5980762114...
Let the inscribed semi circle's radius be a.
b = 2+1
b = 3 units.
b is the diameter of the ascribed semi circle.
c = ½(b)
c = ½(3)
c = (3/2) units.
c = 1.5 units.
c is the radius of the...
a²sin60 = 8
√(3)a² = 16
a = 4/(√√(3)) units.
a = 3.0393427426 units.
a is the side length of the big regular triangle.
b²sin60 = 18
√(3)b² = 36
b = 6/(√√(3)) units.
b = 4.5590141139 units...
Let the square side length be 1 unit.
Therefore, the regular hexagon side length a, is;
a = 5*1
a = 5 units.
b² = 2(5)²-2(5)²cos120
b = 5√(3) units.
Area regular hexagon is;
2(½*5*5s...
