a*3 = 2*6
a = 12/3
a = 4 units.
b = ½(a+3)
b = 3.5 units.
c = ½(2+6)
c = 4 units.
d = c-2
d = 2 units.
It implies, e, radius of the circle is;
e² = 3.5²+2²
e = √(16.25)
e = ½√...
Sir Mike Ambrose is the author of the question.
Let BC be 1 unit.
Therefore;
AB = 2 units.
Area ACDE is;
3²
= 9 square units.
Area purple is;
Area triangle with height 1.2393136...
Let the two equal lengths be a.
b = (4+a) units.
Calculating a.
20² = (4+a)²+a²
400 = 16+8a+2a²
a²+4a+8-200 = 0
a²+4a-192 = 0
(a+2)² = 192+(2²)
a = -2±√(196)
a = -2±14
It implies;
a...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular dodecagon be 1 unit.
Therefore;
The side length square ABCD is;
1 + 2cos30
= (1+√(3)) units.
Area...
3a*a = 4*3
a² = 4
a = 2 units.
sinb = 2/3
b = asin(2/3)°
c = ½(4+3)
c = 3.5 units.
cos(asin(2/3)) = 3.5/d
d = 4.6957427527 units.
d is the radius of the semi circle.
Area semi cir...
a² = 3²+4²
a = √(25)
a= 5 units.
a is the radius of the yellow semi circle.
4² = 2*5²-2*5²cosb
16 = 50-50cosb
50cosb = 50-16
cosb = 34/50
b = acos(17/25)
b = 47.1563569564°
c = 2b
c...
Calculating radius of the inscribed circle.
a² = 4²+4²-2*4*4cos(90-30)
a² = 32-32cos60
a² = 16
a = 4 units.
Let b be the radius of the inscribed circle.
c = (4-b) units.
d = 60-45
d...
Let the two equal lengths be 1 unit each.
a² = 2(1²)
a = √(2) units.
b = 180-60-45
b = 75°
(√(2)/sin45) = (c/sin75)
c = 1.9318516526 units.
d = c-a
d = 0.5176380902 units.
e = 18...
Let a = 1 unit.
b = ½(2+1)
b = 1.5 units.
b is the radius of the semi circle.
c = (1.5-d) units.
d is the radius of the inscribed circle.
e = 2-1.5
e = 0.5 units.
It implies;
(1....
Sir Mike Ambrose is the author of the question.
Let the side length of the square be 10 units.
Area square is;
10²
= 100 square units.
Therefore;
Area R is;
Area semi circle with r...
