Sir Mike Ambrose is the author of the question.
Calculating Yellow Area ÷ Area ABC.
Let the single side length of triangle ABC be 2 units.
Calculating Area ABC.
½(4sin60)
= √(3) square...
Sir Mike Ambrose is the author of the question.
Calculating Area Red ÷ Area Square Exactly.
Let the single side length of the square be 2 units.
Therefore;
Area square is;
2 x 2
= 4 s...
Calculating Shared Area.
a = 7-½(10)
a = 2 cm.
b = ½(10)-r
b = (5-r) cm.
Where r is the radius of the inscribed circle.
Calculating r.
(5-r)² = r²+2²
25-10r = 4
10r = 21
r = 2.1 c...
Calculating area x and y.
a = 16-4
a = 12 units.
tanb = 4/12
b = atan(⅓)°
c = 90-b
c = atan(3)°
d = 180-45-atan(⅓)
d = (45+atan(3))°
It implies;
(e/sin45) = (12/sin(45+atan(3)...
Calculating Length EF (x).
Let a be the radius of the inscribed blue half circle.
b = (4+a) units.
Calculating a.
8²+a² = (4+a)²
64+a² = 16+8a+a²
48 = 8a
a = 6 units.
Again, a is th...
Calculating Pink Shaded Area.
It is;
Area sector with radius 12 units and angle 30°-Area triangle with height 6 units and base 6sin120 units-Area sector with radius 6 units and angle 60°+Area...
Calculating Angle x.
Notice.
Quadrilateral ABCD is a square.
Let AB equal 2 units.
a = (2-y) units.
b = (1+y) units.
b is MQ.
c = (1-y) units.
Where y is the radius of the ins...
Calculating Green Inscribed Triangle.
tana = 12/10
a = atan(6/5)°
b = (180-atan(6/5))
b = (90+atan(⅚))°
c² = 10²+12²
c = √(244)
c = 2√(61) cm.
d = (2√(61)-x) units.
It implies;...
Calculating Area circle ÷ Area semi circle.
Let the radius of yellow circle be r.
Let the radius of the blue semi circle be R.
Calculating r.
It implies;
(4r+1)*1 = 5*1
4r+1=5
4r =...
Calculating yellow area.
r, radius of the inscribed circle is;
r²=(r-4)²+(r-2)²
r²=r²-8r+16+r²-4r+4
r²-12r+20=0
(r-6)²=-20+36
r = 6±√(16)
r = 6±4
Therefore;
r ≠ 2 units....
