Calculating red area.
Red shaded area is;
Area square with single side length 3 inches
= 3 * 3
= 9 square inches.
Sir Mike Ambrose is the author of the question.
Calculating Area Orange.
Radius of the circle, r is;
(5-r)²=18-18cos(180-2atan(4/3))
(5-r)²=12.96
5-r=√(12.96)
5-r=3.6
Therefore...
Sir Mike Ambrose is the author of the question.
Calculating Area yellow ÷ Area purple.
Let the single side length of the regular nonagon be 2 units.
Therefore;
Area purple is;
Area tri...
Sir Mike Ambrose is the author of the question.
Calculating exactly, hatched area ÷ orange area.
Let the ascribed square side length be 2 units.
Therefore, r, radius of the inscribed half...
Sir Mike Ambrose is the author of the question.
Showing that brown area ÷ smaller octagon area = a/b.
Let the side length of the smaller regular octagon be 1 units.
a = ⅛*180(8-2)
a = 135...
Sir Mike Ambrose is the author of the question.
Calculating the exact hatched area.
Let x be the radius of the inscribed circle.
2x² = a²
a = √(2)x cm.
b = x+a
b = (x+√(2)x) cm.
c =...
Calculating Shaded Area (Trapezoid).
It implies;
½ ~ 1
½√(3) ~ x.
Where x is the base of the blue shaded trapezium.
Cross multiply.
½(x) = ½(√(3))
Therefore x = √(3) units.
T...
Calculating Length x.
a = 180-45
a = 135°
Length x is;
x² = (½*5√(2))²+(½*7)²-(½*5√(2)*½*7*2cos135
x = √(½*25+¼*49-½*35√(2)cos135)
x = √((50+49-70√(2)cos135)/4)
x = ½√(99-70√(2)c...
John Horton Conway (b1937)
The Liverpudlian is best known for the serious maths that has come from his analyses of games and puzzles. In 1970, he came up with the rules for the Game of Life, a gam...
Kindly move the question right/left one time to review the framework/analysis.
Thank you nicely.
Calculating area circle.
Let the radius of the circle be r.
r²=2²+(r-1)²
r²=4+r²-2r+1...
