Calculating x.
Let r be the radius of the inscribed green circle.
Let R be the radius of the ascribed quarter circle.
(R-r)² = r²+5² --- (1).
(R-r)²+5² = a² --- (2).
a² = x²+r² --- (3...
Calculating the area of the ascribed regular octagon.
Let the equal longest length of the both inscribed yellow triangles be x.
a = ⅛*180(8-2))
a = ⅛(180*6)
a = ½(45*6)
a = 135°
a is the single in...
Calculating Length AB.
Let AB = (a+7+b) units.
Calculating a and b.
c = (7+b) units.
Therefore;
a(7+b) = 60
a = 60/(7+b) --- (1).
Again.
d = (a+7) units.
Therefore;
b(a+...
Shaded Area is;
Area circle with radius 4 cm - 4(area quarter circle with radius 4 cm - area isosceles right-angled triangle with equal adjacent lengths 4 cm).
= π*4²-4(¼(4²π)-½(4²))
= 16π-4(4π-8...
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...
