Let 1 unit be AB = BC = CD.
a² = 2-2cos150
a = 1.93185165258 units.
a is BD.
b = 90-½(180-150)
b = 90-15
b = 75°
b is angle ABD.
c² = 1+1.93185165258²-2*1.93185165258cos75
c = 1.93185165258 units...
Sir Mike Ambrose is the author of the question.
Calculating Area Shaded ÷ Area Purple to 2 decimal places.
Let AB be 5 units.
Radius, r of the inscribed circle is;
r = 5*(2/5)
r = 2 un...
Calculating Area Blue.
a = 5+3
a = 8 units.
It implies;
b*4 = 3*8
4b = 24
b = 6 units.
b is BC.
c = 4+b
c =10 units.
d² = 10²+5²
d² = 125
d = √(125)
d = 5√(5) unit.
d is the...
Calculating area of the circle.
Let the radius of the circle be r.
Therefore;
(2r)²=2(√(20))²
4r²=40
r = √(10) units.
Therefore area of the circle is;
π√(10)²
= 10π square u...
Calculating R, radius of the inscribed circle.
Let a be the radius of the inscribed half circle.
Calculating a.
b²+9² = 15²
b² = 225-81
b = √(144)
b = 12 units.
c = (12-a) units....
Calculating the inscribed angle beta, let it be y.
Let (x+3) units be the side length of the square.
a²+x² = 4²
a = √(16-x²) units.
b = 1+a
b = (1+√(16-x²)) units.
b is the side length...
Sir Mike Ambrose is the author of the question.
Calculating Area Blue exactly in square units.
Area Blue is;
Area triangle with two side length 10½ units and ((7√(5)sin(atan(3/4)))/(2sin(180...
Calculating the circumference of the blue inscribed circle.
Let x be the base of the inscribed right-angled triangle with height 10 units.
x²+10² = a²
a = √(x²+100) units.
b = ½(a)
b = ½√(x²+100...
Let b = 1 unit.
Therefore;
Side length of the ascribed regular triangle c is;
c = 4b
c = 4(1)
c = 4 units.
Therefore d, radius of the inscribed circle is;
3(4d) = 4√(4²-2²)
12d =...
Calculating Total Shaded Area, Area Grey, Purple and Blue.
Notice.
KLMN is a square.
Calculating area grey.
a = 6-4
a = 2 units.
sinb = 2/6
b = asin(⅓)
b = 19.4712206345°
c²+2² = 6²
c = 4√(2) u...
