Let the two equal lengths be 1 unit.
(a) Calculating Theta exactly.
Let theta be x.
Calculating x.
x = ½(90-54)
x = ½(36)
x = 18°
sin18 = a/1
a = 0.30901699437 units.
b = 90-18...
Let the side of the inscribed square be a.
Calculating a.
a+2√(a²-(a/2)²) = 10√(2)
a+2√(3a²/4) = 10√(2)
2√(3a²/4) = 10√(2)-a
3a² = 200-20√(2)a+a²
2a²+20√(2)a-200 = 0
a²+10√(2)a-100 = 0...
Sir Mike Ambrose is the author of the question.
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)...
Sir Mike Ambrose is the author of the question.
Area Red Total in 1 d. p. Square unit is;
Area Square with side 2√(2) units - Area triangle with height 2√(2) units and base 1.1313708499 units +...
Let the biggest regular pentagon side length be 2 units.
sin72 = a/2
a = 1.90211303259 units.
tan72 = (1.90211303259/b)
b = 0.61803398875 units.
c = 2b
c = 1.2360679775 units.
Where c...
Sir Mike Ambrose is the author of the question.
The side length of the congruent Hexagons is 2 units.
Area hexagon is;
(6*2²)/(4tan30)
= 6√(3)) square units.
a² = 8-8cos30
a = √(8-4√(3)...
Let the side length of the regular pentagon be 4 units.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b = ½(180-a)
b = ½(180-108)
b = 36°
c = 2 units....
Notice.
7 square units is the are of the small pink half circle.
½*a²π = 7
And π = 22/7
½*a²(22/7) = 7
11a² = 49
√(11)a = 7
a = 7√(11)/11 units.
a = 2.110579412 units.
a is the radius...
a² = 4²+3²
a = √(25)
a = 5 units.
a is MN, the side length of the inscribed square.
b² = 2(5²)
b = 5√(2) units.
b is MK, the diagonal of the inscribed square.
tanc = 4/3
c = atan(4/3)°...
Notice.
7 square units is the are of the small pink half circle.
½*a²π = 7
And π = 22/7
½*a²(22/7) = 7
11a² = 49
√(11)a = 7
a = 7√(11)/11 units.
a = 2.110579412 units.
a is the radius...
