Calculating the inscribed half circle's diameter.
Let a be the radius of the inscribed half circle.
b = (1+2a) units.
c = (1+a) units.
d²+a² = (1+a)²
d² = 1+2a+a²-a²
d = √(1+2a) units...
Calculating Angle x.
Let the two equal lengths be 1 unit each.
(a/sin15) = (1/sin30)
a = 0.51763809021 units.
b = 180-(180-15-30)
b = 45°
c² = 1²+0.51763809021²-2*0.51763809021cos45...
Calculating Semicircle's Area.
Let r be the radius of the half circle.
a² = 6²+(½(4))²
a² = 36+4
a = √(40)
a = 2√(10) units.
It implies;
2r² = a²
2r² = (2√(10))²
2r² = 40
r² = 20...
Sir Mike Ambrose is the author of the question.
Area Blue ÷ Area ABC to 2 decimal places.
a = 360-140-80
a = 140°
cos20 = 1/b
b = 1.06417777248 units.
(1.06417777248/sin30) = (c/sin70)...
Calculating Area Yellow Circle.
Let r be the radius of the circle.
r² = 1²+a²-2acos135
r² = 1+a²+√(2)a --- (1).
r² = √(7)²+a²-2√(7)acos45
r² = 7+a²-√(14)a --- (2)
Calculating a.
Eq...
Sir Mike Ambrose is the author of the question.
Calculating Gold Area ÷ Purple Area to 2 decimal places.
Let the side of the regular decagon which is equal the side of the regular octagon be 1...
Calculating Area Blue.
Let x be the radius of the ascribed quarter circle.
a²+5² = x²
a = √(x²-25) units.
a is the diameter of the inscribed circle.
b = ½(a)
b = ½√(x²-25) units.
b is...
Let the width of the square be x.
Therefore the length of the square is 2x.
Calculating x.
x² + x² = (2√(3²+3²)+2(3))²
2x² = (2√(18)+6)²
2x² = (6√(2)+6)²
2x² = 72+72√(2)+36
x² =...
Sir Mike Ambrose is the author of the question.
Calculating Yellow Area ÷ Area ABC.
Let the single side length of triangle ABC be 2 units.
Calculating Area ABC.
½(4sin60)
= √(3) square...
Sir Mike Ambrose is the author of the question.
Calculating Area Red ÷ Area Square Exactly.
Let the single side length of the square be 2 units.
Therefore;
Area square is;
2 x 2
= 4 s...
