Calculating Parallelogram ABCD Perimeter.
4² = x²+y²-2xycos60
16 = x²+y²-xy
16+xy = x²+y² --- (1).
6² = x²+y²-2xycos120
36 = x²+y²+xy
36-xy = x²+y² --- (2).
Equating (1) and (2).
16...
Sir Mike Ambrose is the author of the question.
Calculating Shaded Area ÷ Purple Area to 2 decimal places.
Let AB, side length of the regular octagon be 5 units.
Radius, r of the inscribed...
Calculating Total Inscribed Shaded Area.
Let x be the radius of the five congruent inscribed shaded circle.
a = (14.9-2x) cm.
b = 2x cm.
Calculating x.
(2x)² = x²+(14.9-2x)²
4x² = x...
Calculating Area Blue Inscribed Circle.
Let a be the radius of the blue inscribed circle.
b = (a+5) cm.
c = 12-a-5
c = (7-a) cm.
d = (16-a-5)
d = (11-a) cm.
It implies;
(a+5)² =...
Sir Mike Ambrose is the author of the question.
Calculating Exactly Angle Alpha - Angle Beta.
Let Alpha be x.
Let Beta be y.
(6+6√(2))² = 8²+10²-2*8*10cosa
36+72√(2)+72 = 164-160cosa
1...
Calculating Area Yellow.
a = 22+½(24)
a = 34 units.
Considering a careful, smart analysis of the quarter circle and the inscribed irregular yellow pentagon area.
Therefore, yellow area is;...
Calculating Area Red Inscribed Square.
Let x be the side length of the red square.
a = (5-x) cm.
b = 5-½(x)
b = ½(10-x) cm.
Therefore;
Calculating x.
5² = (5-x)²+(½(10-x))²
25 =...
Sir Mike Ambrose is the author of the question.
Area red in its exact simplest decimal square units form is;
Area triangle with height and base 1.24899959968 units and 1.20185042515 units + A...
Calculating Blue Shaded Area.
tana = 10/6
a = atan(5/3)°
b = 135-a
b = (45+atan(3/5))°
(6/sin(45+atan(3/5))) = (c/sin(atan(5/3)))
c = 5.3033008589 units.
Therefore, required blue are...
Calculating Area Triangle APD.
Let CP be x.
It implies;
x ~ 4
9 ~ x
Cross Multiply.
x² = 36
x = 6 units.
a² = 4²+6²
a = √(16+36)
a = √(52)
a = 2√(13) units.
a is BC, the width o...
