a² = 3²+4²
a = √(25)
a= 5 units.
a is the radius of the yellow semi circle.
4² = 2*5²-2*5²cosb
16 = 50-50cosb
50cosb = 50-16
cosb = 34/50
b = acos(17/25)
b = 47.1563569564°
c = 2b
c...
Calculating radius of the inscribed circle.
a² = 4²+4²-2*4*4cos(90-30)
a² = 32-32cos60
a² = 16
a = 4 units.
Let b be the radius of the inscribed circle.
c = (4-b) units.
d = 60-45
d...
Let the two equal lengths be 1 unit each.
a² = 2(1²)
a = √(2) units.
b = 180-60-45
b = 75°
(√(2)/sin45) = (c/sin75)
c = 1.9318516526 units.
d = c-a
d = 0.5176380902 units.
e = 18...
Let a = 1 unit.
b = ½(2+1)
b = 1.5 units.
b is the radius of the semi circle.
c = (1.5-d) units.
d is the radius of the inscribed circle.
e = 2-1.5
e = 0.5 units.
It implies;
(1....
Sir Mike Ambrose is the author of the question.
Let the side length of the square be 10 units.
Area square is;
10²
= 100 square units.
Therefore;
Area R is;
Area semi circle with r...
Calculating Area Orange.
Let the side length of the inscribed regular triangle be a.
It implies;
2a = 15
a = 7.5 units.
Area sector with radius 15 units and angle 60° - Area regular tr...
Calculating inscribed shaded area green.
a = ⅛*180(8-2)
a = ¼*180*3
a = 135°
a is the single interior angle of the regular octagon.
2b² = 4²
b² = 8
b = 2√(2) units.
c = 2b
c = 4√(2)u...
Let the side length of the square be a.
b²+(0.5a)² = 5²
b = √(25-¼(a²)) units.
c = a-b
c = (a-√(25-¼(a²))) units.
It implies, calculate a.
8² = (0.5a)²+(a-√(25-¼(a²)))²
64 = ¼(a²)+a²...
a = ½(360-2*50)
a = ½(260)
a = 130°
b² = 50²+50²-2*50*50cos130
b = 90.6307787037 units.
sin(0.5*50) = r/c
c = 2.3662015832r units.
sin(0.5*50) = R/d
d = 2.3662015832R units.
It im...
a = (6-b) cm.
b is the radius of the two congruent inscribed yellow half circles.
6 cm is the radius of the ascribed half circle and also, the diameter of the inscribed circle.
c = ½(6)
c =...
