Sir Mike Ambrose is the author of the question.
Area Orange exactly in square cm decimal is;
Area triangle with height 1.64419338427 cm and base (4.95325421888sin129.5411167921) cm
= ½*1.644193384...
a = ⅕(180(5-2))
a = 108°
b = 180-108
b = 72°
sin72 = c/6
c = 5.7063390978 cm.
cos72 = d/6
d = 1.8541019662 cm.
e = 1.8541019662+6
e = 7.8541019662 cm
f² = 7.8541019662²+6²-2*7.8541019662*6cos10...
Sir Mike Ambrose is the author of the question.
Let the side of the regular Pentagon be 2 units.
Therefore;
Area orange is;
Area triangle with height 1.7013016167 unit and base 1.8345763534sin(18)...
Calculating angle x.
Notice!
The ascribed triangle is equilateral.
Let the base of the ascribed triangle be 1 unit.
Observing Sine Rule.
(1/sin(180-20-10)) = (a/sin10)
a = 0.3472963553 units.
Ob...
Let the diameter of the inscribed circle be 1 unit.
Therefore, the radius of the ascribed semi circle is 1 unit.
Calculating angle a°.
b = 0.5 unit.
c = 1.5 units.
Therefore, angle a° is;
atan(...
Let the length and width of the ascribed rectangle be 3 units and 2 units respectively.
Calculating red area.
It is;
Area quarter circle with radius 2 units - Area sector with radius 1.5 units and...
a² = 9
a = √(9)
a = 3 cm.
a is the side of square ABCD.
b² = 3²+3²
b = √(18)
b = 3√(2) cm.
b is AC = BD.
c = ½(b)
c = ½(3√(2))
c = 1.5√(2) cm.
c = AQ = BQ.
Let DE = d.
e = (3+...
Calculating h, height of the ascribed right-angled triangle.
Notice, 4 units is the radius of the inscribed circle.
a² = h²+40²
a= √(h²+1600) units.
a is the hypotenuse of the ascribed right-angle...
Calculating r, radius of the circle.
8² = 9²+7²-2*9*7cosa
cosa = (9²+7²-8²)/(2*7*9)
a = acos((9²+7²-8²)/(2*7*9))
a = 58.4118644948°
(8/sin58.4118644948) = (9/sinb)
b = 73.398450401°
c = ½(180-a)...
Let the side length of the green square be x.
Notice, radius of the two congruent circles is 5 units each.
Therefore;
a = (5-x) units.
b = (5-½(x)) units.
Observing Pythagoras Rule t...
