Blue Area is;
Area square of single side 4cm - 2(area circle of radius 1cm) - 8(area square of single side 1cm) + 8(area quarter circle of radius 1cm).
= 16 - 2π - 8 + ¼(8π)
= 8 - 2π + 2π
=...
Shaded area is;
Area circle with radius 1 units - 8(area quarter circle with radius 1 units - area triangle with height and base 1 units each).
= π - 8(¼(π)-½)
= π - 2π + 4
= (4-π) square u...
Let a be the radius of the quarter circle.
b = ½(a) units.
tanc = b/a
c = atan(½)°
d = atan(2)°
e = d-c
e = (atan(2)-atan(½))°
Therefore, the required length, x is;
tan(atan(2)-...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular hexagon be 1 unit.
Therefore;
Area green is;
Area triangle with height 1 unit and base ⅓√(3) units.
= ½...
Notice;
Triangle ABF is isosceles.
The height is;
4tan(atan¾)
= 3 units.
The base, given is 8 units.
The two equal side length is;
√(4²+3²)
= √(25)
= 5 units.
Radius, r of...
Calculating x, the length that form tangents of the two semi circles.
x²+2²=6²
x²=36-4
x²=32
x = √(32) cm.
x = 4√(2) cm.
Therefore;
Area blue is;
Area trapezium with two parallel le...
Shaded area is;
Area square with side 1542 units - Area equilateral triangle with side 1542 units - 2(area sector with radius 1542 units and angle 30°)
= 1542² - ½(1542)²sin60 - 2(30÷360*1542²...
Calculating R, radius of the bigger circle.
R²=(R-1)²+(R-2)²
R²-6R+5=0
Therefore;
R ≠ 1 units.
R = 5 units.
Its diameter is 10 units.
Calculating r, radius of the big circle.
It wil...
Calculating AB, the diameter of the circle.
Let it be x.
Sin(atan(⅓)) = √(6²+2²)/x
Sin(atan(⅓)) = √(40)/x
x = √(40)/sin(atan(⅓))
x = 20 cm.
x is AB.
Therefore length AC is;
AB - 2...
a = 180-100-50
a = 30°
(20/sin100) = (b/sin30)
b = 10.1542661189 cm
c = ½(180-100)
c = 40°
Let d be the radius of the circle.
tan40 = d/e
e = 1.1917535926d .
f = (10.1542661189-...
