Calculating area of the ascribed circle.
Let r be the radius of the ascribed circle.
a = 3+2
a = 5 units.
a is the side length of the inscribed regular triangle (equilateral triangle).
s...
Calculating Area Orange.
tana = 3/6
a = atan(½)°
sin(atan(½)) = b/3
b = 1.3416407865 units.
cos(atan(½)) = c/3
c = 2.683281573 units.
d = √(6²+3²)
d = √(45)
d = 3√(5) units.
e²...
Notice.
The composite plan shape is not drawn to scale.
Calculating the inscribed orange triangle area.
Notice Again.
3 units is the diameter of the inscribed circle.
a = ½(3)
a = 1.5 uni...
Calculating R, radius of the inscribed circle.
cosa = BA/BC
a = acos(4/8)
a = 60°
a is angle ABC.
b = ½(a)
b = 30°
b is angle ABD = angle CBD.
sin30 = c/8
c = 4 cm.
c is CD.
cos3...
Calculating length BP.
Let CQ = a.
b = (16+a) units.
b is CD = AC, the radius of the ascribed half circle.
c = b-5
c = (11+a) units.
c is BC.
e² = a²+(11+a)²-2a(11+a)cos120
e² = 2a²...
Calculating angle alpha, let it be x.
Let the equal squares side length be 2 units.
2² = 1²+a²
a = √(3) units.
b = a-1
b = (√(3)-1) units.
b = 0.73205080757 units.
sinc = 1/2
c = 30°
tan30 = d/...
Calculating r, radius of a circle.
a = (r-2) cm.
b = (r-1) cm.
It implies;
r² = (r-2)²+(r-1)²
r² = r²-4r+4+r²-2r+1
r²-6r+5 = 0
r²-r-5r+5 = 0
r(r-1)-5(r-1) = 0
(r-1)(r-5)...
Calculating Area Red.
tana = 12/6
a = atan(2)°
b = 90-a
b = atan(½)°
c = 180-2a
c = 2atan(½)°
Red area is;
Area square with side 12 cm - Are ma quarter circle with radius 12 cm -...
Calculating the yellow shaded area.
a² = 2²+4²
a = √(20)
a = 2√(5) cm.
tanb = 2/4
b = atan(½)°
tanc = 4/2
c = atan(2)°
It was;
d = 180-b-c
d = 90°
Shaded yellow area is;
¼...
Calculating x.
a² = 24²+x²
a = √(x²+576) units.
a is the diameter of the ascribed circle.
b = ½(a)
b = ½√(x²+576) units.
b is the radius of the circle.
c = (x-11) units.
d = ½√(x²+5...
