Let the side of the regular pentagon be 1 unit.
Notice;
The regular pentagon side is equal the regular heptagon side.
a = ⅐(180*5)
a = ⅐(900)°, the single interior angle of the regular he...
a² = 11*11+10*10-2*11*10cos50
a = 8.92113926968 cm.
(8.92113926968/sin50) = (10/sinb)
b = 59.16920318624°
c = 180-50-59.16920318624
c = 70.83079681376°
d = 0.5a
d = 4.46056963484 cm....
Area m : Area n is;
(√(2)x)² : (½(3x))²
= 2x² : ¼(9x²)
= 4(2x²) : 4(¼(9x²))
= 8x² : 9x²
= 8 : 9
Area of coloured region is;
Area triangle with height 53.3479501083 m and base 60sin(102.042575143) m + Area triangle with height 100.027406452 m and base √(5924)sin(12.5245961777) m
= (½*53....
Sir Mike Ambrose is the author of the question.
Let beta be x.
x = (½*atan(5/4))
Let alpha be y.
y = (½*atan(4/5))°
Therefore;
Area blue exactly in cm² decimal is;
Area triangle...
a = 360-140-80
a = 140°
cos20 = 1/b
b = 1.06417777248 units.
(1.06417777248/sin30) = (c/sin70)
c = 2 units.
d² = 4+1.064177772482²-4*1.06417777248cos140
d = 2.89711998506 units.
(2.89711998506/...
Sir Mike Ambrose is the author of the question.
Calculating a.
½((0, 6√(3)) (-3, 3√(3)) (a, (16a/3)) (0, 6√(3))) = ¼(9+20√(3))
Therefore;
a = x = ½√(3) units.
y = 16a/3 = (16/3)(√(3)/2...
Let the radius of the ascribed semi circle be 2 units.
Let the radius of the inscribed circle be r.
Calculating r.
(2-r)² = r² + 1
Therefore;
r = ¾ units.
It implies;
OH = r =...
Shaded area is;
Area triangle with height 4√(3) cm and base 8 cm + 2(area sector with radius 8 cm and angle 60° - area triangle with height 4√(3) cm and base 8 cm) - Area circle with radius 2 cm...
Sir Mike Ambrose is the author of the question.
Area green is;
½*3*6sin120
= ½(9√(3)) cm²
Radius, r of the circle is;
r = √(63)/√(3)
r = √(21) cm.
Therefore;
Area circle is;...
