Biggest square side is 14 units.
Bigger square side is 8 units.
a = atan(9/16)
(9/16) = b/c
c = (16b/9) units.
(16b/9)+6 = 14
(16b/9) = 8
b = (9/2) units.
c = (16*9/2)/9
c = 8 units.
d = 9-b
d...
Let the inscribed regular hexagon side length be 1 unit.
a² = 2-2cos120
a = √(3) units.
sin30 = b/1
b = ½ units.
c = 1+b
c = (3/2) units
Calculating r, radius of the ascribed quarter...
Let the side of the regular pentagon be 2 units.
cos36 = a/2
a = 1.61803398875 units.
Where a is the radius of the semi circle.
Area semi-circle is;
½(1.61803398875)²π
= 4.11239817295 square un...
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Let the radius R, of the half circle be 1 unit.
sin30 = c/1
c = ½ units.
c = 0.5 units.
cos30 = d/1
d = ½√(3) units.
d = 0.86602540378 units.
e = 1-0.86602540378
e = 0.13397459622 uni...
Let the height of the yellow area trapezoid be a.
Calculating a.
tan72 = a/b
b = (a/tan72) cm.
c = 2b
c = (2a/tan72) cm.
d = 8+c
d = (8+(2a/tan72)) cm.
It implies;
½*a(8+(8+(2a/tan72))) = 56....
Considering similar triangles ADC and CDB ratios.
Let CD be a.
16 = a
a = 4
Cross Multiply.
a² = 64
a = 8 units
c² = 16²+8²
c = 8√(5) units.
c = AC.
Calculating r1.
16r1+8r1+8√(5)r1 = (16*8)...
Calculating a.
(1/sin120) = (a/sin20)
a = 0.39493084363 units.
Calculating b.
(1/sin120) = (b/sin40)
b = 0.74222719897 units.
Therefore, observing the proof;
(1/a)+(1/b) = 3ab+3
(1/a)+(1/b) is...
Notice;
a² = 5² - (⅕(√(481)))²
a = ⅕(12) units.
b = 5-a
b = ⅕(13) units.
c² = 4²-(⅕(12))²
c = ⅕(16) units.
d = atan(4/3)°
(a) Area A exactly is;
½*⅕(16)*(5+⅕(13)) - atan(4/3)π*16/360
= ((8*38...
Let AB be 1 unit.
BC = 3 units.
It implies;
AC = 1+3
AC = 4 units.
AC is a side length of the square.
Radius of the inscribed half circle a is;
½(BC)
a = ½(3) units.
a = 1.5 units.
b = 1.5+AB
b...
