Calculating red area, area regular hexagon.
Let x be the side length of the red regular hexagon.
a² = 2x²-2x²cos120
a² = 3x²
a = √(3)x units.
b²+3² = x²
b = √(x²-9) units.
sinc = √(x...
Calculating the radius of the ascribed half circle.
Let r be the radius of the semi circle.
Therefore;
A right-angled triangle with hypotenuse 6 units, and adjacent height and base, (r-7)...
Calculating Area Blue.
It implies;
A1 = 64π cm², therefore radius A1, x = 8 cm.
A2 = 32π cm², therefore radius A1, y = 4√(2) cm.
A3 = (16/3)π cm², therefore radius A1, z = 4/√(3) cm....
Sir Mike Ambrose is the author of the question.
Calculating Area yellow ÷ Area green.
Let the side length of the regular hexagon be 1 unit.
Therefore;
Area green is;
Area triangle with...
Let P be the required area.
Calculating P.
a² = 6²+3²
a² = 45
a = √(45)
a = 3√(5) cm.
b = a-x
b = (3√(5)-x) cm.
tanc = 6/3
c = atan(2)°
d = atan(½)
f = 90+d
f = (90+atan(½))...
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...
