Let r be 1 unit.
It implies;
Radius, R of the ascribed semi circle is;
R = 2 units.
2² = a²+(½)²
4-¼ = a²
a = √(15/4)
a = ½(√(15)) units.
1² = b²+(½)²
b² = (3/4)
b = ½(√(3)) units....
Let the side of the regular octagon be 1 unit.
Calculating Area Yellow.
a = ⅛(180*6)-90
a = 45°
b² = 2-2cos45
b = 0.7653668647 units.
c = ½(180-45)
c = 67.5°
d = 135-c
d = 135-67.5
d = 67.5°
It...
Sir Mike Ambrose is the author of the question.
Area Blue, in cm² to 1 d. p. is;
Half area regular pentagon with side 12 cm - area triangle with height 6 cm and base 6tan24 cm - area triangle wit...
Area of the shaded region is;
Area quarter circle with radius 12 units - Area triangle with height and base 12 units respectively - Area quarter circle with radius 8 units + Area triangle with h...
Sir Mike Ambrose is the author of the question.
(a) Exact radius of the circle is;
½√(2²+4²)
= ½√(20)
= ½*2√(5) units.
= √(5) units.
Or
Cos(atan(2)) = (1/r)
Where r is the radius of the...
Let BC be 1 unit.
AB = 2 units.
tan18 = a/2
a = 0.6498393925 units.
a is the radius of the inscribed circle.
Area inscribed circle is;
π(0.6498393925)²
= 1.3266670448 square units.
b = ½(2+1)
b...
sin30 = a/12
a = 6 units.
cos30 = b/12
b = 6√(3) units.
Calculating k.
It implies;
½(2k+6)(6√(3))+(1.5k*(6+k)) = 108+54√(3)
6√(3)k+18√(3)+9k+(3k²/2) = 108+54√(3)
(3k²/2)+(6√(3)+9)k = 108+36√(3)
k...
Let the radius of the ascribed quarter circle be 2 units.
Radius inscribed semi circle is 1 unit.
Therefore;
Area Semi Circle is;
½(π) square units.
Calculate Area Shaded.
tana = ½
a = atan(½)°...
Let the regular triangle side length be 1 unit.
Calculating Area Purple.
(1/sin105) = (a/sin60)
a = 0.8965754722 units.
Area Purple is;
0.5*0.8965754722*1sin45 - ½*½*½
= 0.3169872981-0.125
= 0.1919...
Let the single side length of the regular octagon be 2 unit.
Therefore;
Area green is;
Area triangle with height and base √(2) unit + Area triangle with height 2√(2) unit and base 1 unit - Area t...
