Calculating r/R
Let R = 2 units.
tana = 1/2
a = atan(½)°
b = 90-a
b = atan(2)°
tan(0.5atan(2)) = r/c
½(1+√(5))-1 = r/c
½(√(5)-1) = r/c
c = 2r/(√(5)-1)
c = ½(1+√(5))r units.
d =...
Calculating r, radius of the inscribed circle.
tana = 10/5
a = atan(2)°
sin30 = r/b
b = 2r units.
c = (10-r) units.
Calculating r.
(10-r)² = 5²+(2r)²-10*2rcos(30+atan(2))
100-20...
Calculating r, radius of the circle.
a = 3+17+4
a = 24 units.
a is the diameter of a half circle.
b = ½(a)
b = 12 units.
b is the radius of the half circle.
c = (12-r) units.
d = ½(...
Sir Mike Ambrose is the author of the question.
Calculating Area Blue ÷ Area Red Exactly.
Let the ascribed quarter circle radius be 4 units.
Therefore;
Area blue is;
Area triangle with...
Calculating Area Inscribed Blue Square.
a² = 4²-2²
a = √(12)
a = 2√(3) units.
b = 2a
b = 4√(3) units.
Let x be the side length of the inscribed blue square.
x+c+c = 4
x+2c = 4 --- (...
Calculating Area Green.
Let r be the radius of the ascribed quarter circle.
a²+1² = r²
a² = r²-1
a = √(r²-1) cm.
a is the diameter of the white inscribed circle.
b = ½(a)
b = ½√(r²-1)...
Calculating Area S, Yellow Area.
a = 20 units.
a is the radius of the quarter circle.
b = 2a
b = 40 units.
c²+20² = d²
d = √(c²+400) units.
e = 7+d
e = (7+√(c²+400)) units.
Calcu...
Calculating x.
a² = 24²+x²
a = √(x²+576) units.
a is the diameter of the ascribed circle.
b = ½(a)
b = ½√(x²+576) units.
b is the radius of the circle.
c = (x-11) units.
d = ½√(x²+5...
Calculating area yellow.
12 ~ a
(12+6) ~ 6
Cross Multiply.
12*6 = 18a
a = 4 units.
Therefore, yellow area is;
½*12*6 - ½*4*6 - ½*6*3
= ½(72-24-18)
= ½(72-42)
= ½(30)
=...
Sir Mike Ambrose is the author of the question.
Calculating Area Green Total.
Area green total exactly in decimal cm² is;
Area triangle with two side (12-6√(3)) cm each and angle 60° + Are...
