Sir Mike Ambrose is the author of the question.
Area blue exactly is square units decimal form is;
½(Area triangle with height (2√(2)+2√(2+√(3))) units and base 12.9282032303sin75 units - Area...
Radius, r of one of the five congruent, inscribed circles is;
8r²+√(3)r-1=0
r = (√(35)-√(3))/16 m.
Therefore;
Total area of the five congruent, inscribed yellow circles is;
5πr²
=...
a² = 4²+3²
a = √(25)
a = 5 units.
a is MN, the side length of the inscribed square.
b² = 2(5²)
b = 5√(2) units.
b is MK, the diagonal of the inscribed square.
tanc = 4/3
c = atan(4/3)°...
since tanx = 3/4, it implies;
Let AB = 4 units.
Let AD = 3 units.
tana = 4/3
a = atan(4/3)°
a is angle ADB.
b = 180-a
b = 90+90-atan(4/3)
b = (90+atan(3/4))°
b is angle BDC.
It...
Sir Mike Ambrose is the author of the question.
Area Gold exactly in square cm decimal form is;
Area trapezium with two parallel side 6√(13) cm and 14.9769052981 cm, and height 11.6487041207 cm...
Let the two equal inscribed right-angled triangle side lengths be a each.
Calculating a.
0.5a² = 50
a² = 100
a = 10 units.
a is EU.
Notice!
Arc TU = Arc US.
Let b be the radius of...
Blue area is;
½(2.5)²π - (180-2atan(3/4))π(2²)/360 + 0.5*2²sin(180-2atan(3/4)) - (180-2atan(4/3))π(1.5)²/360 + 0.5*1.5²sin(180-2atan(4/3)) + ½(4*3) - 2atan(4/3)π(1.5²)/360 + 0.5(1.5²)sin(2atan(4...
Let the side of the regular pentagon be 1 unit.
Calculating Area Red.
a² = 1²+1²-2*1*1cos108
a = 1.61803398875 units.
b = 108-36-60
b = 12°
(c/sin12) = (1.61803398875/sin96)
c = 0.33...
Sir Mike Ambrose is the author of the question.
Let the side of the square be 2 units.
Therefore;
Area square is;
2²
= 4 square units.
Area S is;
Area triangle with two side 0.9892...
Let the square side be 2 units.
tan30 = a/2
a = ⅓(2√(3)) unit.
sin60 = 2/b
b = ⅓(4√(3)) units.
c = 2-a
c = ⅓(6-2√(3)) units.
It implies;
Area Shaded is;
2(½*(⅓(6-2√(3)))²sin60)...
