Calculating Red Area.
A nice and careful examination of the irregular pentagon, makes a regular quadrilateral (square) with side length 1 cm.
It implies;
Red area is;
1²
= 1*1
= 1 cm²...
Calculating Yellow Area.
Let a be the side length of the square.
b = ½(a) units.
c² = a²+(½(a))²
c² = ¼(5a²)
c = ½√(5)a units.
c is the radius of the half circle.
It implies;
a ~ ½√(5)a
d ~ a
C...
Calculating Yellow Area.
a = ½(24)
a = 12 units.
b² = 12²+c²
c = √(b²-144) units.
Where;
b is the ascribed half circle's radius.
c is the inscribed half circle's radius.
Area yellow i...
Calculating R, radius of the circle.
Notice.
3 units is the side length of the inscribed yellow square.
2 units is the side length of the inscribed red square.
1 unit is the side length of the i...
Calculating Shaded Area.
Notice.
a = ½(4)
a = 2 cm.
a is the radius of the inscribed circle.
tanb = 4/2
b = atan(2)°
c = 90-b
c = atan(½)°
d² = 2²+4²
d = √(20) cm.
d = 2√(5) cm...
Calculating x.
a = 23+x+3
a = (26+x) units.
b = 23-3
b = 20 units.
Length x is;
21²+20² = (26+x)²
441+400 = 676+52x+x²
x²+52x-165 = 0
(x+26)² = 165+26²
(x+26)² = 676+165
(x+26)²...
Area Pink is;
¼(π*3²)-½(3²)+3((¼π)-½)
= ¼(9π)-½(9)+¼(3π)-½(3)
= ¼(12π)-½(12)
= 3π-6
= 3(π-2) square units.
Calculating x.
Notice.
AC = BC
Let a be alpha.
It implies;
sina = 0.5x/(1+4)
sina = ⅒(x) --- (1).
Again.
sina = 1/x --- (2).
Equating (1) and (2).
⅒(x) = 1/x
x² = 10
x...
Calculating the area of the ascribed half circle.
Let a be the radius of the circle.
b² = a²+(3√(3))²
b = √(a²+27) units.
c = ½(3+b)
c = ½(3+√(a²+27)) units.
d = c-3
d = ½(3+√(a²+27))-3
d = ½(√(...
Calculating red Area.
Notice.
3x = 4-x
4x = 4
x = 1 unit.
Where x is the radius of the red quarter circle and the inscribed white half circle.
y = 4-x
And x = 1 units.
y = 4-1
y = 3...
