Calculating x, the base of the ascribed right-angled triangle.
a² = 15²+x²
a = √(15²+x²) units.
a is the hypotenuse of the ascribed right-angled triangle.
Therefore, x is;
3*15+3*x +3√(1...
Calculating the required angle, let it be x.
Let a be the side length of the equilateral triangle.
It implies;
6² = a²+10²-2*10*a cosy
36 = a²+100-20acosy
20acosy = a²+64
cosy = (a²+64)/...
Calculating Area Circle Green.
Let x be the radius of area circle green.
a²+2² = x²
a = √(x²-4) units.
b = a+x
b = (x+√(x²-4)) units.
Calculating x.
(x+√(x²-4)) ~ 2
8 ~ √(x²-4)...
Calculating the red length. Let it be x.
Notice.
AB = CD = 2 units.
It implies;
AD = 2((AB)+½(AB))
AD = 2*(2+½(2))
AD = 2(2+1)
AD = 6 units.
a²+(2+1)² = 6²
a² = 36+9
a = √(27)...
Calculating Shaded Area.
Shaded blue area is
Area quarter of radius 10 cm - Area sector of radius 10 cm and angle 30° - Area equilateral triangle of single side length 5 cm - Area sector of...
Calculating Area Circle.
Radius of the circle r is;
r = 5-(√(18-18cos(180-2atan(4/3)))
r = 5-3.6
r = 1.4 units.
r = (7/5) units.
Therefore area of the circle is;
πr²
= π(7/5...
Calculating red area.
Red shaded area is;
Area square with single side length 3 inches
= 3 * 3
= 9 square inches.
Sir Mike Ambrose is the author of the question.
Calculating Area Orange.
Radius of the circle, r is;
(5-r)²=18-18cos(180-2atan(4/3))
(5-r)²=12.96
5-r=√(12.96)
5-r=3.6
Therefore...
Sir Mike Ambrose is the author of the question.
Calculating Area yellow ÷ Area purple.
Let the single side length of the regular nonagon be 2 units.
Therefore;
Area purple is;
Area tri...
Sir Mike Ambrose is the author of the question.
Calculating exactly, hatched area ÷ orange area.
Let the ascribed square side length be 2 units.
Therefore, r, radius of the inscribed half...
