Calculating BD/AC.
Let 1 unit be AB = AD.
a = 180-30-30
a = 120°
a is angle BAD.
b² = 2-2cos120
b = √(2-2cos120)
b = √(3) units.
b is length BD.
c = 180-15-45
c = 120°
c is angle...
Calculating x, the required angle.
Let the side length of the regular pentagon be 1 unit.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b² = 1²+0.5²-2*1*...
Calculating shaded yellow area.
Let x be the side length of the ascribed regular decagon.
Let y be the side length of the two equal inscribed regular pentagons.
a = ⅒*180(10-2)
a = 144°...
Calculating Angle Alpha.
Let 2 units be the radius of the half circle.
sina = 1/2
a = 30°
b = 90-a
b = 60°
It implies, the required angle alpha is, let it be c.
c = 45+b
c = 45+60...
Calculating the required area.
Let it be y.
a = x cm²
b = (50-x) cm²
c = 60-b
c = 60-(50-x)
c = (10+x) cm²
d = 40-c
d = 40-(10+x)
d = (30-x) cm²
It implies;
y = d+x
y = (3...
Calculating y, the red required angle.
It implies;
½*πr² = 32π
r = √(64)
r = 8 cm.
r is the radius of the half circle.
2r = 16 cm, the diameter of the half circle.
Let x be the radiu...
Calculating Area Shaded.
Let r be the radius of the ascribed half circle.
Therefore;
½(r) is the radius of the inscribed circle and also the height of the shaded area.
a = r+½(r)
a = ½...
Calculating Area Blue Inscribed Circle.
Let it's radius be x.
a = ½(16)+x
a = (8+x) units.
b = (8-x) units.
c = (16-x) units.
It implies;
d²+x² = (16-x)²
d² = 256-32x+x²-x²
d =...
Sir Mike Ambrose is the author of the question.
Calculating Exactly Green Area.
Let x be the side length of each of the three inscribed congruent squares.
a² = 2x²
a = √(2)x
a is the diago...
Calculating FB.
a = 8+9
a = 17 units.
b = 9-8
b = 1 unit.
c² = 17²+1²
c = √(290) units.
c = 17.0293863659 units.
c is DE.
2d² = c²
2d² = √(290)²
d² = 145
d = √(145) units.
d =...
