Calculating green area.
a = (6+x) units.
a is the radius of the circle.
b = a-2
b = (6+x)-2
b = (4+x) units.
(6+x)² = (4+x)²+c²
36+12x+x² = 16+8x+x²+c²
c² = 20+4x
c = √(20+4x) units....
Let the required angle be x.
5 units, 3 units and 2 units are the radii respectively of each of the circles, decreasingly.
Calculating x.
a = 5+2
a = 7 units.
b = 5-2
b = 3 units....
Sir Mike Ambrose is the author of the question.
Calculating Area Purple ÷ Area Rectangle.
Let the single side length of the three side regular hexagon be 1 unit.
Therefore;
The width of t...
Calculating Length x (AC).
Notice.
BC = AD = 9 units.
a = 9+7
a = 16 units.
a is BD.
It implies;
9² = 15²+16²-2*15*16cosb
81 = 225+256-480cosb
480cosb = 481-81
cosb = 400/480
b...
Calculating Blue Area.
a = (14-x) cm.
Calculating x.
10² = x²+(14-x)²
100 = x²+196-28x+x²
2x²-28x+96 = 0
x²-14x+48 = 0
x²-6x-8x+48 = 0
x(x-6)-8(x-6) = 0
(x-6)(x-8) = 0
It implies;...
Calculating area of the circle.
Let x be the radius of the circle.
Method 1.
It implies;
2*(4+2) = 6*a
6a = 12
a = 2 units.
b = 6+2
b = 8 units.
It implies, a cyclic regular qu...
Calculating r, radius of the circle.
a = ½(14)
a = 7 units.
b = (r-7) units.
r² = 7²+c²
c² = r²-49
c = √(r²-49) units.
It implies, 6 units, b and c will make a right-angled triangle where 6 unit...
Calculating angle x.
Notice.
AC = BC.
Let AB be 1 unit.
(1/sin(180-70-60-20)) = (a/sin(60+20))
a = 1.96961550602 units.
a is AE.
(1/sin(180-70-10-60)) = (b/sin60)
b = 1.3472963553...
Calculating the area of the ascribed regular octagon.
Let the equal longest length of the both inscribed yellow triangles be x.
a = ⅛*180(8-2))
a = ⅛(180*6)
a = ½(45*6)
a = 135°
a is the...
Calculating Shaded Area.
a = 2+3
a = 5 units.
b = 4+3
b = 7 units.
tanc = 7/3
c = atan(7/3)°
d² = 2(2)²
d = 2√(2) units.
tane = 5/(3-2)
e = atan(5)°
f = 180-e
f = (180-atan(...
