Calculating p.
2² = (½(3p)+p)²+(½(p))²
4 = (5p/2)²+(p/2)²
4 = (25p²/4)+(p²/4)
4 = ¼(26p²)
16 = 26p²
p = √(16/26)
p = √(8/13) units.
p = 0.7844645406 units.
It implies;
a = ½(3p)
a = 0.5*3*0.784464...
Calculating r, radius of the inscribed circle.
a = ½(108)
a = 54°
a is half the single interior angle of the regular pentagon.
tan54 = r/b
b = r/tan54
b = 0.726542528r units.
r is the radius...
Let the side length of the three congruent regular hexagon be 1 unit.
a = ⅙(180(6-2))
a = 120°
a is the single interior angle of the three congruent regular hexagon.
b² = 2-2cos120
b = √(3)...
Let the side of the ascribed regular hexagon be 1 unit.
a = ⅙(180(6-2))
a = 120°
a is the single interior angle of the ascribed regular hexagon.
b² = 1²+1²-2*1*1cos120
b = √(3) units.
b is the hei...
Calculating r, radius of the smaller semi circle.
Radius of the bigger semi circle a, is;
a = ½(3+7+2)
a = 6 units.
6² = r²+b²
36-r² = b²
b = √(36-r²) units.
c = 6-3.5-2
c = 0.5 units.
b² = d²+0...
Notice.
The composite plane shape consist of two regular plane shapes, a square and an equilateral triangle.
Let the four congruent units of the square be 1 each.
It implies a, the square s...
Notice!
AB = AC
It implies, triangle ABC is isosceles.
a = 180-45-30
a = 105°
a is angle ADC.
b = ½(180-45)
b = ½(135)
b = 67.5°
b = angle ABC = angle ACB
c = 67.5-45
c = 22.5°
c is angle DBE....
Area green is;
6(2(area sector with radius 4 units and angle 60°-area triangle with height 4 units and base 4sin60 units.))
= 6(2((60π*4*4/360)-(½*4*4sin60)))
= 6(2(⅓(8π)-4√(3)))
= 12(⅓(8π)-4√(3))...
Let a be the radius of the inscribed circle.
Let the circle's centre be X.
Calculating a.
(3-a)² = √(3)²+a²
9-6a+a² = 3+a²
6 = 6a
a = 1 unit.
a is the radius of the inscribed circle (XT = XN = XE...
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