Calculating angle x.
Let the two equal lengths of the ascribed square be 1 unit.
tan10 = 1/a
a = 5.6712818196 units.
a is the square side considering the assume 1 unit.
b = a-1-1
b = 5.6712818196...
Calculating r, radius of the two congruent circles.
It implies;
(2r)² = (2+r)²+1-2(2+r)cos60
4r² = 4+4r+r²+1-2-r
3r² = 3+3r
r²-r-1 = 0
Resolving the above quadratic equation via completing the sq...
Calculating area red.
a = 4+6 = 10 units.
a is the side length of the two congruent regular composite plane shape.
b = ½(10)
b = 5 units.
c = 5-1
c = 4 units.
tans = 4/6
d = atan(2/3)°
e² = 6²+...
Let the centre of the semi circle be O.
Let d be 2a.
It implies, a is the radius of the semi circle.
a = OA = OB
(2a)² = b²+7²
b² = 4a²-49
b = √(4a²-49) units.
c = ½(b)
c = ½√(4a²-49) units.
e...
Let the radius of the bigger green quarter circle be 1 unit.
Let the radius of the smaller green quarter circle be a.
Let the radius of the circle be b.
It implies;
b² = 1²+a²-2acos45
b² = 1+a²-...
Notice!
The congruent triangles are equilateral.
Calculating the radius, a of the two bigger congruent circles.
tan60 = a/b
√(3) = a/b
b = (a/√(3)) units.
sin60 = 2a/c
√(3)/2 = 2a/c
√(3)c = 4a
c...
Notice!
Area Yellow is an equilateral triangle with side 2 units.
Therefore, area yellow is;
½*2*2sin60
= √(3) square units.
Calculating red area.
It is;
2(area quarter circle with radius 2 uni...
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)...
