Let the square side be 1 unit.
Area Square is;
1² = 1 square unit.
Calculating Area Blue.
a = 108-60-36
a = 12°
b = 180-12-108
b = 60°
1 = 2c²-2c²cos108
1 = 2.6180339887c²
c = 0.6180339887 unit...
Let the side length of the regular pentagon be 1 unit.
a = ½(108)-25
a = 54-25
a = 29°
b = 72-29
b = 43°
(c/sin108) = (1/sin43)
c = 1.3945143742 units.
tan25 = d/1.3945143742
d = 0....
Let the regular hexagon side length be a.
Calculating a.
0.5a²sin120 = 4√(3)
√(3)a² = 16√(3)
a = 4 units.
b² = 4²+4²-2*4*4cos120
b = 4√(3) units.
c = ½(b)
c = 2√(3) units.
d² = 2²+4²-2*2*4cos12...
a² = 6²+18²-2*6*18cos150
a = 23.3893455919 cm.
(23.3893455919/sin150) = (18/sinb)
b = 22.6307402124°
tan22.6307402124 = c/6
c = 2.5013366786 cm.
Area Red exactly in decimal is;
0.5*2.5013366786*...
Sir Mike Ambrose is the author of the question.
Let the single side length of the congruent regular hexagons be 1 unit.
Therefore;
Area red is;
Area trapezium with two parallel side length ½(3√(...
sin30 = a/10
a = 5 cm.
b = 10+2a
b = 20 cm.
c² = 20²+4²-160cos60
c = 4√(21) cm.
c = 18.3303027798 cm.
(18.3303027798/sin60) = (20/sind)
d = asin(5√(7)/14)°
d = 70.8933946491°
e = 180-d
e = (180-...
Sir Mike Ambrose is the author of the question.
Let the side of square ABCD be x.
Calculating x.
½*x(x+½(x)) = 84+24
½(½(3x²)) = 108
¼(x²) = 36
x² = 36*4
x = 12 cm.
Notice;
The base of blue area...
Blue area is;
8(area quarter circle with radius 4 cm - area triangle with height and base 4 cm each) - 8(area quarter circle with radius 2 cm - area triangle with height and base 2 cm each)
= 8(4π...
Let the red length be a.
Calculating a.
b² = 8²+8²
b = 8√(2) units.
c² = 2²+2²
c = 2√(2) units
d = 8√(2)-2√(2)-2-½(a)
d = ½(12√(2)-4-a) units.
e² = 2a²-2a²cos120
e² = 3a²
e = √(3)a units.
Equ...
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