Sir Mike Ambrose is the author of the question.
Calculating Exact Area Blue.
Let the small inscribed square side length be x.
The big inscribed square side length will be 2x.
Calculating...
Calculating r, radius of the half circle.
a = 2r units.
a is the diameter of the half circle.
b = ½(2r-4)
b = (r-2) units.
c²+(r-2)² = (4√(3))²
c²+r²-4r+4 = 48
c² = 44+4r-r²
c = √(44+...
Calculating Red Area.
a²+68² = 85²
a² = 7225-4624
a = √(7225-4624)
a= 51 units.
Let b be the radius of the circle.
Calculating b.
*68b+51b+85b* = 68*51
b = (68*51)/(68+51+85)
b =...
Sir Mike Ambrose is the author of the question.
Calculating Purple Area ÷ Yellow Area.
Let the side of the regular pentagon be 1 unit.
Therefore;
Area purple is;
Area trapezium with tw...
Calculating b/a.
Let x be the side length of the square.
Therefore;
a+b = x
c² = 15²+8²
c² = 225+64
c = √(289)
c = 17 units.
d²+x² = 17²
d = √(289-x²) units.
e = x-d
e = (x-√...
Sir Mike Ambrose is the author of the question.
Calculating the exact shaded area.
Notice;
Square side is 4 units.
Small regular hexagon side is 2 units.
Big regular hexagon side is 4 units.
T...
Calculating A+B Area.
a = 2*3√(2)
a = 6√(2) units.
a is the diagonal of the square.
2b² = 2a²
2b² = (6√(2))²
2b² = 2*36
b = √(36)
b = 6 units.
b is the side length of the square.
Ca...
Calculating the area of the inscribed circle.
Notice.
The inscribed triangle is equilateral.
Let x be the radius of the inscribed circle.
a = (12-x) cm.
It implies;
tan30 = x/(12-...
Calculating the circumference of the inscribed circle.
Let x be the radius of the inscribed circle.
a = (4.5+x) units.
b = (4.5-x) units.
c²+x² = (4.5-x)²
c² = ¼(81)-9x+x²-x²
c² = ¼(8...
Calculating the required red rectangle area.
a = √(4) = 2 units.
b = √(16) = 4 units.
c = √(9) = 3 units.
d = a+b
d = 2+4
d = 6 units.
e = b-a
e = 4-2
e = 2 units.
f² = 6²+2²...
