Calculating Blue Area.
Let a be the congruent inscribed side lengths each of the inscribed right-angled isosceles triangle.
b = ½(2)
b = 1 unit.
c²+1² = a²
c = √(a²-1) units.
d = ½(18...
Calculating Area Purple ÷ Area Orange Exactly.
Area purple is;
Area trapezoid with two parallel sides 4 cm and (50/9) cm, and height (7/2) cm - Area triangle with height 4 cm and base 3 cm....
Calculating angle alpha, let it be x.
Let R = 2 units.
a = (2-r) units.
Calculating r.
It implies;
r²+r² = (2-r)²
2r² = 4-4r+r²
r²+4r-4 = 0
(r+2)² = 4+(2)²
r = -2±√(8)...
Calculating the required angle, let it be x.
Let 1 unit be the side length of the both congruent inscribed equilateral triangles.
a = ⅑*180(9-2)
a = 140°
a is the single interior angle of t...
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)...
