Let the regular octagon side be 2 units.
Area Octagon is;
½(8*2)*(2/(2tan(180/8)))
= 8/(tan(180/8))
= 19.31370849898 square units.
Calculating Area Red.
a = ⅛(180*6)
a = 135°
Le...
a² = R²+6²
a = √(R²+36) units.
a is OB.
b = a-4
b = (√(R²+36)-4) units.
c = 6+4
c = 10 units.
It implies;
10² = R²+(√(R²+36)-4)²
100 = R²+R²+36-8√(R²+36)+16
48 = 2R²-8√(R²+36)
8√...
Let the single side length of the two congruent inscribed regular pentagon be 1 unit.
Area Green is;
0.5*5(1/(2tan(180/5)))
= 1.72047740059 square units.
Calculating Area Shaded.
a = ⅕...
Let a be the big inscribed circle radius.
Let b be the bigger inscribed circle radius.
Let c be the biggest inscribed circle radius.
It implies;
a+b = 12 --- (1).
a+c = 22 --- (2)....
(x⁶-1)/(x⁴-x) = 2
((x³+1)(x³-1))/(x(x³-1)) = 2
(x³+1)/x = 2
x³-2x+1 = 0
For x = 1
x³-2x+1 = 0
Therefore;
(x-1) is a factor of x³-2x+1
Calculating the other values of x.
(x³-2x+1)/(...
Calculating the area of the red rectangle.
Let a be the radius of the half circle.
b = ½(a) units.
Calculating a.
a² = (½(a))²+1²
a² = ¼(a²)+1
(3/4)a² = 1
a² = 4/3
a = √(4/3)
a = ⅓...
Calculating red area.
a = (1+x) units.
a is the diameter of the circle.
b = ½(a)
b = ½(1+x) units.
b is the radius of the circle.
c = ½(1-x) units.
Calculating x.
(½(1+x))² = (½(1...
Calculating x, the side length of the ascribed square.
tana = 14/7
a = atan(2)°
b = 90+a
b = (90+atan(2))°
c² = 14²+7²
c² = 196+49
c = √(245) units.
c = 7√(5) units.
d² = √(245)²+9...
a = 8+2
a = 10 units.
a is OA, the radius of the half circle.
b = 2a
b = 20 units.
b is AB, the diameter of the half circle.
c = 2+a
c = 12 units.
c is BC.
Notice.
BC = BD = 12 un...
Calculating x.
Let a be the radius of the ascribed quarter circle.
b = 4+4
b = 8 units.
Notice.
BD = 4 units.
OB = x+BD
OB = (x+4) units.
OB is the radius of the ascribed quarter...
