Calculating yellow area.
a = ½(270)-90
a = 135-90
a = 45°
Notice.
CD = BD = 23 units.
Let b be the radius of the quarter circle.
c = 2b units.
c is the diameter of the circle....
Let a be the radius of the inscribed semi circle.
Calculating a.
b² = 9²+9²
b² = 162
b = 9√(2) cm.
b is the diagonal of a square.
c = (9+a) cm.
It implies:
(9+a)² = a²+(9√(2))²-2*...
Calculating inscribed blue square area.
a² = 8²+8²
a = 8√(2) units.
b = a-8
b = (8√(2)-8) units.
Let c be the inscribed square side length.
d² = 2c²
d = √(2)c units.
e = a-d
e =...
Notice.
Triangle ABC is isosceles.
Let BC be 1 unit.
It implies;
(1/sin24) = (a/sin(48+30))
a = 2.4048671724 units.
a is AB = AC.
b = 180-24-42-48
b = 180-114
b = 66°
b is angle...
Cross multiply.
5x-3(4-x) = 20x
Expand.
5x-12+3x = 20x
Collect like terms and simplify.
-12 = 12x
Divide both sides by 12, the coefficient of x.
x = -1
Checking accuracy....
a = ½(21-11)
a = ½(10)
a = 5 units.
sinb = 5/13
b = asin(5/13)
b = 22.619864948°
c = b+90
c = 112.619864948°
c is angle ABC = angle BCD.
d = ½(360-2c)
d = ½(134.7602701039)
d = 67....
Notice!
Since angle CDN and angle DNM are equal, it implies;
AN = one third the side length of the square.
AN = ⅓(3+3)
AN = ⅓(6)
AN = 2 m.
Therefore, yellow area is;
Area square with...
Calculating R, radius of the inscribed circle.
Let a be the radius of the ascribed semi circle.
b = (2a-4) units.
c = (a-4) units.
a² = c²+d²
a² = (a-4)²+d²
d² = a²-(a²-8a+16)
d² = 8a-16
d = √(8...
tan60 = h/a
a = ⅓√(3)h m.
b = 100+a
b = (100+⅓√(3)h) m.
tan30 = h/(100+⅓√(3)h)
√(3)h = (100+⅓√(3)h)
3√(3)h = 300+√(3)h
2√(3)h = 300
√(3)h = 150
h = 50√(3) m.
Sir Mike Ambrose is the author of the question.
Area Square is:
√(40)²
= 40 square units.
Area Green is;
Area triangle with two lengths 4√(10) units and 6√(5) units, and angle 45°, the...
