Calculating area of the circle.
Let x be the radius of the circle.
Method 1.
It implies;
2*(4+2) = 6*a
6a = 12
a = 2 units.
b = 6+2
b = 8 units.
It implies, a cyclic regular qu...
Calculating r, radius of the circle.
a = ½(14)
a = 7 units.
b = (r-7) units.
r² = 7²+c²
c² = r²-49
c = √(r²-49) units.
It implies, 6 units, b and c will make a right-angled triangle where 6 unit...
Calculating angle x.
Notice.
AC = BC.
Let AB be 1 unit.
(1/sin(180-70-60-20)) = (a/sin(60+20))
a = 1.96961550602 units.
a is AE.
(1/sin(180-70-10-60)) = (b/sin60)
b = 1.3472963553...
Calculating the area of the ascribed regular octagon.
Let the equal longest length of the both inscribed yellow triangles be x.
a = ⅛*180(8-2))
a = ⅛(180*6)
a = ½(45*6)
a = 135°
a is the...
Calculating Shaded Area.
a = 2+3
a = 5 units.
b = 4+3
b = 7 units.
tanc = 7/3
c = atan(7/3)°
d² = 2(2)²
d = 2√(2) units.
tane = 5/(3-2)
e = atan(5)°
f = 180-e
f = (180-atan(...
Calculating radius of the circle.
Let x be the diameter of the circle.
a²+x² = (3+1)²
a = √(16-x²) units.
It implies;
√(16-x²) ~ ½(x)
(3+1) ~ 2√(3)
Cross Multiply.
2√(48-3x²) =...
Calculating Triangle ADE.
a² = (3√(3))²+(4√(3))².
a² = 27+48
a = √(75)
a = 5√(3) units.
a is AC.
3√(3)b+4√(3)b+5√(3)b = 3√...
Calculating Triangle ADE.
a² = (3√(3))²+(4√(3))².
a² = 27+48
a = √(75)
a = 5√(3) units.
a is AC.
3√(3)b+4√(3)b+5√(3)b = 3√(3)*4√(3...
Calculating ratio Red length to Blue length.
a² = 2(1)²
a = √(2) units.
a is the side length of the bigger square.
tanb = 1/(1+1)
b = atan(½)°
c = 45-b
c = (45-atan(½))°
tan(45-atan...
Calculating Area ABCD (square).
Notice.
The green triangle is an isosceles right-angled triangle.
Let the side length of the square be x.
Calculating x.
(x/sin45) = (a/sin(180-45-30))...
