Let the base of the equilateral be 1 unit.
a = 180-22-16-38
a = 180-76
a = 104°
(1/sin104) = (b/sin38)
b = 0.6345091075 units.
c = 180-16-44-38
c = 180-98
c = 82°
(1/sin82) = (d/si...
Shaded region/area is;
2(sector area with radius 2cm and angle 60°) - (equilateral triangle area with sides 2cm each side) + (square area with sides 2cm each side) - (square area with sides 4cm...
Sir Mike Ambrose is the author of the question.
Exact Area R in its simplest from will be;
Area semi circle with radius 2 unit - Area right-angled triangle with height 2√(2+√(2)) unit and wid...
a = 5+√(7)-1
a= (4+√(7)) units.
tanb = 1/(4+√(7))
b = atan(1/(4+√(7)))
c = 2b
c = 2atan(1/(4+√(7)))°
cos(2atan(1/(4+√(7)))) = (5+√(7))/d
d = (5+√(7))/cos(2atan(1/(4+√(7))))
d = 8 unit...
Let the three equal lengths of the ascribed pentagon be 1 unit each.
a² = 2-2cos80
a = 1.2855752194 units.
b = ½(180-80)
b = 50°
c = 80-b
c = 30°
d = 90-b
d = 40°
It implies;...
a = ⅛*180(8-2)
a = 135°
a is the single interior angle of the regular octagon.
b² = 2²+2²-2*2*2cos135
b = 3.69551813 units.
c = 135-2*½(180-135)
c = 135-45
c = 90°
d = 90-½(45)
d = 9...
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the regular hexagon.
b = a-90
b = 30°
tan30 = 6/c
c = 6/(1/√(3))
c = 6√(3) cm.
Therefore, area orange is;
½*6*c
= ½*6*6√(...
Let a be the radius of the quarter circle.
It implies;
a² = a²+4²-2*a*4cosb
8cosb = 16
acosb = 2
cosb = 2/a --- (1).
8² = a²+4²+2*a*4cosb
64 = a²+16+8acosb
48 = a²+8acosb --- (2)....
Notice!
The regular polygon has 12 sides (regular dodecagon).
a = (180(12-2))/12
a = 1800/12
a = 150°
a is the single interior angle of the regular dodecagon.
b = ½(a)
b = 75°
c = 90-b...
Let AB = AC = 1 unit.
It implies;
a² = 2-2cos(24+12)
a = 0.6180339887 units.
a is BC = AD.
b = ½(180-24-12)
b = ½(144)
b = 72°
b is angle ACB = angle ABC.
c² = 0.6180339887²+1-2*0....
