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...
Calculating Area Inscribed Blue Square.
a² = 4²-2²
a = √(12)
a = 2√(3) units.
b = 2a
b = 4√(3) units.
Let x be the side length of the inscribed blue square.
x+c+c = 4
x+2c = 4 --- (...
Calculating the length of the blue region.
Notice.
a = ½(10)
a = 5 units.
a is the radius of the inscribed circle.
tanb = 10/5
b = atan(2)°
c = 90-b
c = atan(½)°
d = 45-c
d = (4...
Calculating Area Triangle AED.
Let x be CD.
Figuring an equilateral triangle OCD considering the strategic given two equal angles, 60°.
a = (x-8) units.
a is DE.
b = (x-10) units.
b is...
Calculating Area Green.
Let x be the radius of the half circle.
a = ½(8)
a = 4 units.
x = (4+b) units.
Recall, x is the radius of the half circle.
c²+4² = (4+b)²
c² = 8b+b²
c = √(8b...
