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....
Sir Mike Ambrose is the author of the question.
Calculating Red Shaded Area ÷ Blue Shaded Area to 2 decimal places.
Let the side of the regular pentagon be 1 unit.
a = 360-2(108)-90
a = 54°...
Sir Mike Ambrose is the author of the question.
Calculating Shaded Area ÷ Green Area to 2 decimal places.
Let the side of the regular pentagon be 1 unit.
a = 108-90
a = 18°
b = 180-108-...
Calculating Blue Area.
Area Blue (Star) is;
Area circle of radius 20 cm - 5(area triangle with two length 14.5308505601 cm and angle 108°, the angle they form) - 5(Area sector of radius 20 cm...
Sir Mike Ambrose is the author of the question.
Calculating Shaded Area ÷ Green Area to 2 decimal places.
Let the single side length of the two congruent inscribed regular pentagon be 1 unit....
Calculating Area Triangle ABC.
Let CM be x.
Calculating x.
x+1 ~ x+3
1 ~ 2
Cross multiply.
2x+2=x+3
x = 1 unit.
Therefore,
CM = 1 unit.
Therefore angle C will be;...
