Let AC be 1 unit.
Area smaller pentagon is;
½(5)*(1/(2tan(36)))
= 1.72047740059 square units.
a² = 1²+0.5²-cos108
a = 1.24860602048 units.
Where a is CD.
(1.24860602048/sin108) =...
Sir Mike Ambrose is the author of the question.
Area R is;
Area triangle with height 4 cm and base (4tan52.5) cm - Area sector with angle 52.5° and radius 4 cm.
= ½*4(4tan52.5) - (52.5*4*4π)...
a² = 10²+16²-2*10*16cos120
a = 2√(129) units.
Where a is length AC.
(3√(129)/sin120) = (16/sinb)
b = 37.58908946897°
c = 90-b
c = 52.41091053103°
d = 60-b
d = 22.41091053103°
e...
Let the radius of the inscribed half circle be 1 unit.
Area rectangle is;
2*1
= 2 square units.
Calculating Shaded Area as a single fraction..
It is;
½(1*2) - 1² + ¼(1)²π - ((180-2a...
Let the two congruent lengths be 1 unit.
tan40 = a/1
a = 0.83909963118 unit.
cos40 = 1/b
b = 1.30540728933 units.
Calculating r, radius of the red inscribed circle.
(r/tan(20)) + (r/t...
Let the radius of the semi circle be 1 unit.
cos20 = a/2
a = 1.87938524157 units.
cos20 = 1/b
b = 1.06417777248 units.
c = a-b
c = 0.81520746909 unit.
Where c is AB, the side of the...
Let the side of the regular pentagon be 1 unit.
Calculating Area Red.
a² = 1²+1²-2*1*1cos108
a = 1.61803398875 units.
b = 108-36-60
b = 12°
(c/sin12) = (1.61803398875/sin96)
c = 0.33...
a² = 15²+12²-2*12*15cos120
a = 23.43074902772 cm.
Where a is the side length of the equilateral triangle ABC.
(23.43074902772/sin120) = (12/sinb)
b = 26.32950349168°
c = 60-b
c = 33.67...
Sir Mike Ambrose is the author of the question.
Let the side length of triangle ABC be 1 unit.
a = 120-78
a = 42°
b = 60-42
b = 18°
(1/sin42) = (c/sin18)
c = 0.4618186516 unit.
tan6...
a² = 12²+6²
a = 6√(5) cm.
a = AE.
b = atan(1/2)°
b = angle DAE.
c = 180-atan(2)
c = 116.56505117708°
c = angle AFC.
d = 180-116.56505117708-atan(1/2)
d = 36.86989764584°
(6/sin36....
