Calculating angle x.
Let 1 unit be the side length of the square.
Let y be the equal red lengths.
It implies;
a = (1-y) units.
b² = y²+1²
b = √(y²+1) units.
c² = 1²+1²
c² = 2
c...
Sir Mike Ambrose is the author of the question.
Area Purple ÷ Area ABCD (square) in its simplest form.
Let the single side length of the regular dodecagon be be 1 unit.
Therefore;
Area pu...
Sir Mike Ambrose is the author of the question.
Calculating Total Area Red.
Area Red Total in 1 decimal place square units is;
Area Square with side 2√(2) units - Area triangle with height 2...
Sir Mike Ambrose is the author of the question.
Point P coordinate is;
P(4, -3)
Point R coordinate is;
R(0, ⅓(37))
Point Q (maximum turning point) coordinate is;
Q((-3√(259)/14),...
Sir Mike Ambrose is the author of the question.
Calculating Area Aqua.
Area Aqua, in square units to 2 d. p. is;
Area triangle with two side 5 units and 6 units, and angle acos(0.2)° - Area triang...
Calculating the chord length.
Let x be the radius of the half circle.
a = (x-4) units.
b = (x-9) units.
c = (x-7) units.
d = a+b
d = (x-4)+(x-9)
d = (2x-13) units.
d is the length...
Calculating FM ÷ ML.
Let 2 units be the side length of square.
Calculating FM.
tana = 2/1
a = atan(2)°
a is angle AFB.
Let b, be the radius of the small inscribed circle.
c = (1-b)...
Calculating area of the square.
Let x be the side length of the square.
7² = x²+3²-2*x*3cosy
49 = x²+9-6xcosy
6xcosy = x²-40
cosy = (x²-40)/(6x) --- (1).
5² = x²+3²-2*x*3cos(90-y)
25 =...
Calculating Area Orange ÷ Area Large Square.
Let length AB be 3 units.
Therefore;
AC = 20 unit.
It implies;
Area large square is;
20²
= 40 square units.
Area orange is;
A...
Calculating Area Square ÷ Area Enclosed S
Let the side of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
Area S is;
Area triangle with two side 0.989218...
