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...
Calculating Shared Area.
a = 7-½(10)
a = 2 cm.
b = ½(10)-r
b = (5-r) cm.
Where r is the radius of the inscribed circle.
Calculating r.
(5-r)² = r²+2²
25-10r = 4
10r = 21
r = 2.1 c...
Calculating area x and y.
a = 16-4
a = 12 units.
tanb = 4/12
b = atan(⅓)°
c = 90-b
c = atan(3)°
d = 180-45-atan(⅓)
d = (45+atan(3))°
It implies;
(e/sin45) = (12/sin(45+atan(3)...
Calculating Length EF (x).
Let a be the radius of the inscribed blue half circle.
b = (4+a) units.
Calculating a.
8²+a² = (4+a)²
64+a² = 16+8a+a²
48 = 8a
a = 6 units.
Again, a is th...
Calculating Pink Shaded Area.
It is;
Area sector with radius 12 units and angle 30°-Area triangle with height 6 units and base 6sin120 units-Area sector with radius 6 units and angle 60°+Area...
