Calculating the area of each rectangle.
Let the length and width of the rectangle be y and z respectively.
Therefore;
7+7+x+y+z+7+7+x+y+z=66
Where 7 is the single side length of the squar...
Sir Mike Ambrose is the author of the question.
Calculating Area Orange ÷ Area Triangle ABC.
Let the single side length of the regular hexagon be 2 units.
Therefore;
Area orange is;
1.25264388762...
Sir Mike Ambrose is the author of the question.
Let alpha be x.
Calculating Cot²x and (Red length ÷ Blue length)² as single fractions.
Let the side length of the square be 2 units.
tan30...
Calculating Red Area.
Let x be length AB equal length BD.
a²+3² = x²
a = √(x²-9) units.
It implies;
Calculating x
½(4+x)*3 = (3*x)+½(3√(x²-9))
12+3x = 6x+3√(x²-9)
12-3x = 3√(...
Calculating Length x.
a = 12+8
a = 20 units.
cosb = 20/24
b = acos(5/6)°
c = 90-b
c = (90-acos(5/6))°
c = 56.4426902381°
Therefore, the required length x is;
cos56.4426902381 = 8/x
x = 8/cos56...
Sir Mike Ambrose is the author of the question.
Calculating Blue Area + Red Area Exactly.
Let x be the side length of the regular octagon.
a = ⅛*180(8-2)
a =135°
a is the single interior a...
Calculating angle x.
a = 180-2(58)-48
a = 180-116-48
a = 180-164
a = 16°
a is angle BAD.
Let 1 unit be the let AB equal length AC.
(a')² = 2-2cos(a+48)
a' = √(2-2cos64)
a' = 1.059838...
Calculating Area Inscribed Green Circle.
Let a be the radius of the inscribed green circle.
b = 8-2
b = 6 units.
tanc = 6/8
c = atan(3/4)°
d = ½(90+c)
d = ½(90+atan(3/4))°
e = (2-a) units.
It...
Calculating Required Shaded Area.
Notice.
The three circles are congruent.
Therefore, the required shaded area is;
Area equilateral triangle with side r units+3(area sector with radius r...
Sir Mike Ambrose is the author of the question.
Calculating Area Blue.
It is;
Area triangle with height 25 units and base ⅓(100) units - Area square with single side length 5 units - Area...
