sin60 = a/20
a = 10√(3) cm.
a+b = 20
b = (20-10√(3)) cm.
c = 20-2b
c = 20-2(20-10√(3))
c = 20-40+20√(3)
c = (20√(3)-20) cm.
c = 14.64101615138 cm.
Therefore;
Shaded Area Red is;
½(14.641016151...
Notice;
Radius r of the circle is 6 units.
Area Red is;
6(area sector with radius 6 units and angle 6°-area triangle with base 6 units and height 6sin60 units)
= 6(60π*36/360 - ½*36sin60)
= 6(6π-...
Let the the side length of the inscribed hexagon side 2 units.
a² = 2-2cos120
a = √(3) units.
a = 1.73205080757 units.
a is the side length of the inscribed square.
Therefore;
Area Square is;
a²...
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Let AB be 2 units.
a = atan(½)°
b² = 2²+1²
b = √(5) units.
Let r be the radius of the inscribed circle.
Calculating r.
sin(atan½) = r/c
c = r/sin(atan½) units.
It implies;
1+r+(r/sin(atan½))...
Let r be the radius of the inscribed semi circle.
Calculating r.
r² = (r-4)²+(r-8)²
r² = r²-8r+16+r²-16r+64
r²-24r+80 = 0
It implies;
r ≠ 4 cm.
r = 20 cm.
a² = 20²+16²
a = 4√(41) cm.
(4/sinb) =...
Area Shaded exactly in square units as a single fraction is;
Area triangle with height 6√(3) units and base 6 units - Area triangle with height 2√(3) units and base 2 units - Area sector with radiu...
Let the side of the equilateral triangle be 2 units.
Let the side of the square be a.
Calculating a.
tan60 = a/1
a = √(3) units.
Area square is;
a²
= √(3)²
= 3 square units.
Calculating area...
Let the shortest length of the composite plane shape be 1 unit.
(1/sin12) = (a/sin153)
a = 2.18357369878 units.
(2.18357369878/sin27) = (b/sin99)
b = 4.75051853365 units.
c² = 4.75051853365+1-2*4...
Let the a side length of the yellow regular triangle be 2 units.
Therefore, a side length of the regular pentagon is 2 units.
Area Yellow is;
0.5*2*2sin60
= 2sin60
= √(3) square units.
= 1.732050...
