Notice;
The radius, a of the small inscribed circle is;
a = 2 units.
Calculating b, radius of the big circle.
c² = 8²+8²
c = √(128)
c = 8√(2) units.
d² = 2²+2²
d = √(8)
d = 2√(2) units.
It impl...
Let the regular triangle side length be 2 units.
Therefore the square side length is 1 unit.
a² = 2(1²)
a = √(2) units.
b² = 2+1-2√(2)cos105
b = √(3-2√(2)cos105) units.
(√(3-2√(2)cos105)/sin105)...
Sir Mike Ambrose is the author of the question.
Let R be radius of the inscribed circle.
Calculating r.
√(100-25) = r+√(25+r²)
r = ⅓(5√(3)) cm.
Therefore;
Area Shaded as a single fract...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular hexagon be 1 unit.
Area Hexagon is;
(½(6))(1/(2tan(180/6)))
= 3/2tan(30)
= ½(3√(3)) square units.
Notice;
1/sin...
Sir Mike Ambrose is the author of the question.
Let the bigger regular pentagon side length be 1 unit.
a = √(2-2cos180)
a = 1.61803398875 units.
b = sin36/sin108
b = 0.61803398875 units.
c = √(2*...
Sir Mike Ambrose is the author of the question.
Area Blue exactly in cm² decimal form is;
Area trapezoid with two parallel side (7√(2)+14) cm and 15.3137084989 cm, and height 18.4852813742 cm.
= ½...
Sir Mike Ambrose is the author of the question.
Area Green is;
Area triangle with height √(8(31-14√(3))) units and base √(178-72√(3))sin57.72115346403 units.
= 0.5*√(8(31-14√(3)))*√(178-72√(3))sin5...
Sir Mike Ambrose is the author of the question.
Let the radius of the semicircle be 1 unit.
Area Semicircle is;
½*1²*π
0.5π square units.
Calculating AC = AB = BC
sin67.5 = (AC)/1
AC = sin67.5 un...
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tan30 = a/(2√(3))
a = 2 units.
b = (2√(3)-2) units.
tan30 = c/(2√(3)-2)
c = ⅓(6-2√(3)) units.
d = 2√(3)-⅓(6-2√(3))
d = ⅓(6√(3)-6+2√(3))
d = ⅓(8√(3)-6) units.
It implies;
Area Blue exactly in sq...
