Calculating radius of the semi circle.
Radius, r of the semi circle is;
Cos(2atan(1/(4+√(7))))=(5+√(7))/d
Notice;
d = 2r
Therefore,
d = (5+√(7))/Cos(2atan(1/(4+√(7))))
d = 8 un...
Calculating Area Blue Fraction.
Let the radius of inscribed blue semi circle be 2 units.
Therefore the radius of the inscribed blue quarter circle will be 2 units.
The length of the ascrib...
Calculating Area Quadrilateral ABCD.
Notice.
A right-angled triangle is derived considering quadrilateral ABCD with interior angles 40°, 50° and 90°.
AD = 1 unit.
BC = 3 units.
Let AB...
Sir Mike Ambrose is the author of the question.
Calculating Area R ÷ Area large square.
Let the single side length of the large square be 2 units.
Therefore;
Area large square is;
2...
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...
