Radius of the green circle is 4 units, therefore area of the green circle is;
π4²
= 16π square units.
Calculating radius of the red circle.
Let the radius of the red circle be r.
(4-...
Let 1 unit be the side length of the regular hexagon.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the regular hexagon.
cos75 = 0.5/b
b = 1.93185165258 units.
c² = 1²+0.5²-...
Let the three equal inscribed lengths be y.
a = 5+4
a = 9 units.
a is the radius of the ascribed half circle.
b² = y²+y²
b = √(2)y units.
Notice.
a = b
√(2)y = 9
y = ½(9√(2)) uni...
Sir Mike Ambrose is the author of the question.
Let the radius of the semi circle be 3 units.
Therefore shaded area ÷ area square will be;
(½(area quarter circle of radius 3 units - area tri...
Let the radius of the ascribed quarter circle be R.
Let the radius of the inscribed circle be r.
Therefore;
2²+(2r)²=R²
4+4r²=R²
Therefore;
R²-4r²=4
Multiplying through by ¼(π)...
Let a be the side length of the two equal inscribed lengths.
r = 2+1
r = 3 units.
r is the radius of the ascribed half circle.
b²+(a/2)² = 3²
b²= 9-¼(a²)
b = √(9-¼(a²))
b = ½√(36-a²) unit...
a = (10+x) units.
a is the radius of the half circle.
(10+10)² = 16²+b²
b = √(400-256)
b = √(144)
b = 12 units.
It implies;
12 ~ c
20 ~ 10
Cross Multiply.
20c = 120
c = 6 units...
Let the radius of the circle be a.
sinb = a/(a+a)
b = 30°
cos30 = c/2a
c = √(3)a units.
d = 2-c
d = (2-√(3)a) units.
sin30 = e/d
e =½(2-√(3)a) units.
cos30 = f/d
½√(3) = f/(2-√(...
Sir Mike Ambrose is the author of the question.
Area S exact, or to 3 d.p. will be;
Area sector of radius 2√(7) units and angle (180 - 2sin–¹(4sin120÷(2√(7)))) + area triangle of two lengths 2...
Let the radius of the red circle be r.
Calculating r.
It will be;
√(13²-5²)=√((9+r)²-(9-r)²)+√((4+r)²-(4-r)²)
12=√(36r)+√(16r)
12=10√(r)
√(r)=1.2
r=1.44 units.
Calculating a...
