Notice;
AB = 25 units.
cos30 = 8√(3)/a
a = 16 units.
tan30 = b/(8√(3))
b = 8 units.
Let the side of the regular hexagon be c.
c = ¼(AC)
Calculating AC.
((AC)/sin46) = (25/sin74...
Calculating green inscribed triangle area.
a² = 2(3√(2))²
a² = 2*18
a = √(36)
a = 6 units.
a is AB.
b = ½(360-90)
b = ½(270)
b = 135°
b is angle ABC.
c² = 6²+(4√(2))²-2*6*4√(2)cos13...
Calculating the required angle, alpha.
Let it be a.
Let R = 2 units, radius of the ascribed semi circle.
b = (2-r) units.
It implies;
Calculating r.
(2-r)² = 2r²
2-r = √(2r²)
2-...
9^(x)+9*9^(x) = 270
Let 9^(x) be p.
p+9p = 270
10p = 270
p = 27
And p = 9^(x)
9^(x) = 27
2x = 3
x = 3/2
x = 1.5
7² = 3²+8²-2*3*8cosa
48cosa = 9+64-49
a = acos((9+64-49)/48)
a = 60°
Calculating b, radius of the inscribed circle.
3b+8b+7xb = 3*8sin60
18b = 12√(3)
3b = 2√(3)
b = ⅔√(3) units.
b = 1....
Sir Mike Ambrose is the author of the question.
Let the side of the regular pentagon be 1 unit.
Therefore;
Area purple is;
Area trapezium with two parallel side 0.07294901687 units and 0....
Notice;
Green regular hexagon's side is 8 cm.
sin60 = a/8
a = 4√(3) cm
Where a is the the height of the white triangle enclosed by the two green regular hexagon and the regular pentagon....
Radius of the circle, r is;
√(2-2cos120)
r = √(3) units.
Therefore!
Area yellow is;
Area regular hexagon with side 2 units - 2(area triangle with height ½ units and base √(3) units) -...
Let the base of the triangle ascribing the green and yellow area b 1 unit.
tan55 = a/1
a = 1.42814800674 units.
tan55 = b/(1-b)
b = 0.58816349035 units.
Where b is the side of the white...
Sir Mike Ambrose is the author of the question.
Notice;
Square side is 4 units.
Small regular hexagon side is 2 units.
Big regular hexagon side is 4 units.
Therefore;
Area shaded, exa...
