Let the green square side be 1 unit.
Area Green Square is;
1²
= 1 square units.
Calculating the total shaded area.
a² = 1²*2
a = √(2) units.
a is the radius of the quarter circle.
tan15 = b/1
b...
Sir Mike Ambrose is the author of the question.
Let the side of the regular pentagon be 1 unit.
It implies;
Radius large circle, R is;
= 0.580673 unit.
Radius small circle, r is;
= 0.168821 unit....
tan30 = 6/a
a = 6√(3) units.
b = (4+6√(3)) units.
b is the square side.
Let the side length of the inscribed regular hexagon be x (Red Length).
Calculating x.
c = (120-atan(⅔))°
d = 120-c
d = a...
Our certified, experienced, resilient, productive and committed Math Educators will be glad to be at your service.
We make teaching and learning Mathematics fun for learners, we expose the simplicit...
Let AB = 1 unit.
Therefore;
BC = 2AB = 2 units.
It implies;
AD = 4 units.
Calculating Area Red.
a² = 2²+1-2*2cos(180-(900/7))
a = 1.58304794386 units.
(1.58304794386/sin(180-(900/7))) = (2/sinb)...
Sir Mike Ambrose is the author of the question.
Let the side length of the large square be 1 unit.
2a² = 1
a = ½√(2) unit.
b² = ½+1-√(2)cos(360-195)
b = 1.69293396321 units.
(1.69293396321/sin(36...
Let the side length of the congruent yellow regular hexagon be 1 unit.
a = 3sin30+1
a = 2.5 units.
sin60 = b/1
b = 0.5√(3) units.
c² = a²+b²
c² = 2.5²+(0.5√(3))²
c = √(7) units.
c = 2.64575131106...
Sir Mike Ambrose is the author of the question.
The vertices coordinates of area purple are;
(6, 12) ((24/5), (36/5)) ((180/29), (168/29)) (12, (21/2))
Area purple is;
½((6, 12) ((24/5), (...
Calculating equation of the curve.
y-6√(2) = a(x-6)² --- (1).
Substituting x = 0, y = 0 to get a.
It implies;
-6√(2) = 36a
a = -(1/(3√(2)) --- (2).
Substituting (2) in (1).
y-6√(2) = -(1/(3√(2))(...
Sir Mike Ambrose is the author of the question.
Let the side of the ascribed regular pentagon be 2 units.
(a) Calculating alpha. Let it be x.
a² = 5-4cos108
a = 2.49721204096 units.
(2.4972120409...
