Let the side of the regular pentagon be 1 unit.
a = 360-2(108)-90
a = 54°
tan72 = b/0.5
b = 1.53884176859 units.
tan54 = 1.53884176859/c
c = 1.11803398875 units.
d = c-0.5
d = 0.618...
Notice;
The diameter of the semicircle is 8 units.
Therefore radius is 4 units.
tan30 = a/2
a = ⅔(√(3)) units.
b = 3a
b = 2√(3) units.
c² = 2²+(⅔(√(3)))²
c = (4/√(3)) units.
d...
Let the side of the regular hexagon which is equal the side of the square be 1 unit.
a = ½(180-108)
a = 36°
tan36 = b/0.5
b = 0.363271264 unit.
Area Blue is;
0.5*0.363271264*0.5
=...
Sir Mike Ambrose is the author of the question.
Let the side of the inscribed square be 2 units.
Therefore;
Area S is;
Area triangle with two side 1.03528 units and 0.53589838486 units, and angl...
Sir Mike Ambrose is the author of the question.
P coordinate is;
P(3, 9)
Q coordinate is;
Q(2, 5), Q(3, 5)
It implies;
Shaded area exactly in its square units simplest form is;
(...
Sir Mike Ambrose is the author of the question.
Calculating the circle's radius, r.
21r + 15r + 12√(2)r = 21*12√(2)sin45
(36+12√(2))r = 252
r = 252/(36+12√(2)) cm
r = 3(3-√(2)) cm
I...
Sir Mike Ambrose is the author of the question.
Let the radius of the ascribed semicircle be 2 units.
Therefore;
Radius of the inscribed circle is 1 unit.
It implies;
Area R is;
Are...
Let a be the side of the square.
cos30 = b/8
b = 4√(3) cm.
sin30 = c/8
c = 4 cm.
a = b+12
a = (12+4√(3)) cm.
Area Square is;
a²
= (12+4√(3))²
= 358.27687752661 cm²
d² = 12²+4²...
Let the single side length of the two congruent inscribed regular pentagon be 1 unit.
Area Green is;
0.5*5(1/(2tan(180/5)))
= 1.72047740059 square units.
Calculating Area Shaded.
a =...
Sir Mike Ambrose is the author of the question.
Area Orange exactly in square cm decimal is;
Area triangle with height 1.64419338427 cm and base (4.95325421888sin129.5411167921) cm
= ½*1.644...
