Calculating Blue Shaded Area.
tana = 10/6
a = atan(5/3)°
b = 135-a
b = (45+atan(3/5))°
(6/sin(45+atan(3/5))) = (c/sin(atan(5/3)))
c = 5.3033008589 units.
Therefore, required blue are...
Calculating Area Triangle APD.
Let CP be x.
It implies;
x ~ 4
9 ~ x
Cross Multiply.
x² = 36
x = 6 units.
a² = 4²+6²
a = √(16+36)
a = √(52)
a = 2√(13) units.
a is BC, the width o...
Sir Mike Ambrose is the author of the question.
Calculating Green Area to 3 significant figures.
Notice.
8 cm is the side length of the regular nonagon and also the regular bigger inscribe...
Calculating x.
Let r be the radius of the inscribed green circle.
Let R be the radius of the ascribed quarter circle.
(R-r)² = r²+5² --- (1).
(R-r)²+5² = a² --- (2).
a² = x²+r² --- (...
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*...
