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Sir Mike Ambrose is the author of the question.
Calculating Blue Area Exactly.
Calculating Area Brown.
a = (180(12-2))/12
a = 1800/12
a = 300/2
a = 150°
a is the single interior angle of...
Calculating Area Square.
Let x be the side length of the square.
a²+x² = 13²
a = √(169-x²) cm
b = x-a
b = (x-√(169-x²)) cm.
c² = 2x²
c = √(2)x
c is the diagonal of the square.
C...
Calculating Area Shaded.
a = (x+6) cm.
a is the radius of the ascribed circle.
b = a-8
b = (x+6)-8
b = (x-2) cm.
c = b+a
c = (x-2)+(x+6)
c = (2x+4) cm.
c is the diameter of the inscr...
Sir Mike Ambrose is the author of the question.
Let the side length of the square be 10 units.
Area square is;
10²
= 100 square units.
Therefore;
Area R is;
Area semi circle with...
Calculating Area Blue.
a = √(9)
a = 3 units.
a is the side length of the big square.
b = √(16)
b = 4 units.
b is the side length of the bigger square.
It implies;
½*3*4sinx = 3
12...
x/y = golden ratio (½(1+√(5)).
Therefore, the prove.
Let the side length of the regular pentagon be 1 unit.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon....
Sir Mike Ambrose is the author of the question.
Calculating Red Area ÷ Area ABCD Exactly.
Let the side length of the regular dodecagon be 1 unit.
Therefore;
The side length square ABCD...
Calculating red area, area regular hexagon.
Let x be the side length of the red regular hexagon.
a² = 2x²-2x²cos120
a² = 3x²
a = √(3)x units.
b²+3² = x²
b = √(x²-9) units.
sinc = √(x...
Calculating the radius of the ascribed half circle.
Let r be the radius of the semi circle.
Therefore;
A right-angled triangle with hypotenuse 6 units, and adjacent height and base, (r-7)...
