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;...
Calculating Area Blue Inscribed Circle.
a = (x+1) units.
b = (4-x) units.
It implies;
(x+1)² = 1²+(4-x)²
Where x is the radius of the inscribed blue circle.
Calculating x.
x²+2...
Sir Mike Ambrose is the author of the question.
Calculating Area purple ÷ Area brown exactly.
Area purple is;
Area trapezium with two parallel side length (58/15) cm and (46/5) cm, and hei...
Calculating Angle x.
Let the base of the ascribed quadrilateral be 1 unit.
(1/sin78) = (a/sin(18+30))
a = 0.75974712295 units.
(1/sin78) = (b/sin54)
b = 0.82709091529 units.
(0.827090...
Calculating Ascribed Square Area.
Let the ascribed square side length be x.
a² = 5
a = √(5) cm.
a is the side length of the inscribed red square.
b² = 20
b = √(20)
b = 2√(5) units.
b...
Calculating x, the base of the ascribed right-angled triangle.
a² = 15²+x²
a = √(15²+x²) units.
a is the hypotenuse of the ascribed right-angled triangle.
Therefore, x is;
3*15+3*x +3√(1...
