Calculating Area Green.
Let x be the side length of the ascribed square.
a = ½(x) units.
tanb = x/(½(x))
b = atan(2)°
c = 180-45-atan(2)
c = (45+atan(½))°
It implies;
(0.5x/sin(...
Calculating Angle x.
Let AC = 1 units.
sin(10+10) = a/1
a = 0.34202014333 units.
a is BC.
tan40 = b/0.34202014333
b = 0.28698897612 units.
c = 180-10-30-40
c = 100°
(1/sin100) =...
Calculating Yellow Area.
2a² = 2²
a = √(2) units.
a is the radius of each of the two congruent half circles.
2b² = (2+1)²
b² = ½(9)
b = ½(3√(2)) units.
b is the radius of the circle....
Calculating angle x.
a = 180-2(48)
a = 180-96
a = 84°
b = 180-72-a
b = 180-72-84
b = 180-156
b = 24°
c = ½(180-72)
c = ½(108)
c = 54°
d = 90-c
d = 90-54
d = 36°
Therefore, t...
Calculating Area Blue.
a = 5+3
a = 8 units.
a is the side length of the big square.
b² = 3²+8²
b² = 9+64
b = √(73) units.
c = ½(b)
c = ½√(73) units.
c is the side length of the two e...
Calculating Shaded Area Blue.
a² = 4²+3²
a = √(25)
a = 5 units.
a is the radius of the quarter circle.
5 ~ 4
3 ~ b
Cross Multiply.
5b = 12
b = 2.4 units.
d² = 5²+3²
d = √(34) units...
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...
