Sir Mike Ambrose is the author of the question.
Let Alpha be x.
Calculating x;
½(180-atan2)-atan(0.5)
x = ½(90-atan(0.5))
It implies;
tan x exactly is;
= tan(½(90-atan(0.5)))
Calculating Area Oran...
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Sir Mike Ambrose is the author of the question.
Notice;
Side length of the congruent regular hexagon is 2 units.
(a) Calculating
Length Blue ÷ Length Red.
Length Blue is;
Let it be x.
4²=2²...
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Sir Mike Ambrose is the author of the question.
Calculating k.
3k² = 108
k = 6 units.
The equation of the curve is;
y = 4x-⅓(x²)
Area R is;
Area under the curve at x=0 and x=(6-3√(2)).
= 2(6-3√(2)...
Sir Mike Ambrose is the author of the question.
Let the side of the regular quadrilateral (square) be 4 units.
Area square is;
4²
= 16 square units.
Area Red is;
Area triangle with height 4.562952...
tana = 4/8
a = atan(½)°
b = (180-2atan(½))°
It implies;
Area Orange is;
Area triangle with base 8 units and height 4 units - Area square with side 4 units + Area quarter circle with radius 4 unit...
Sir Mike Ambrose is the author of the question.
Let the side of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
Radius of the inscribed circle, r is;
sin52.5 = r/1.044209537...
Sir Mike Ambrose is the author of the question.
Let the side of the regular hexagon be 2 units.
Therefore;
Area Green is;
Area regular equilateral triangle with side √(3) units.
½*√(3)*√(3)sin60
=...
