Notice!
BD is the diameter of the circle.
a = ½(BD)
a = ½(14)
a = 7 cm.
a is OB = OD.
a is the radius of the circle.
b = 2(45)
b = 90°
b is angle AOB.
Calculating shaded area....
0.5*4*5sina = 8
Where a is the supplementary angle of angle ABC.
It implies;
10sina = 8
a = asin(8/10)
a = asin(4/5)°
or
a = acos(3/5)°
or
a = atan(4/3)°
a = 53.1301023542°
Therefo...
Notice!
The radius of the quarter circle is 4 units.
4² = 2²+a²
16-4 = a²
a = √(12)
a = 2√(3) units.
It implies, area green is;
Area triangle with height 2√(3) units and base 2 units...
Notice!
The side length of the small inscribed square is twice the side length of the big inscribed square.
Let the side length of the small inscribed square be a units
Therefore, the sid...
Area red is;
Area rectangle with length 4 units and width 3 units - Area triangle with height 4 units and base 1 unit - Area rectangle with length 2 units and width 1 unit - Area triangle with h...
Let a be the radius of the half circle.
a²+8² = b²
b = √(a²+64) units.
b is OC.
Observing similar plane shape (right-angled) side length ratios.
8 - c
√(a²+64) - a
Cross Multiply.
c =...
a²+1.5² = 4²
a² = 16-2.25
a = 3.7080992435 units.
tanb = a/1.5
b = atan(3.7080992435/1.5)
b = 67.9756871627°
b is angle ODC.
c = 90-b
c = 22.0243128373°
c is angle ODT.
It implies;...
Sir Mike Ambrose is the author of the question.
The base/length of the rectangle with height or width 4 units is 3√(3) units.
Therefore calculating red area (right-angled triangle with hypotenu...
a = (4-x) units.
It implies;
4² = (4-x)²+2²
12 = 16-8x+x²
x²-8x+4 = 0
(x-4)² = -4+(-4)²
(x-4)² = -4+16
(x-4)² = 12
x = 4±√(12)
x = 4±2√(3)
It implies;
x = (4-2√(3)) units.
a = (4-x)...
a = (b+1) units.
a is the diameter of the circle.
c = ½(a)
c = ½(b+1) units.
c is the radius of the circle.
d² = 1+1
d = √(2) units.
d is the diagonal of a square.
e = d-c
e = √(2)-½(...
