Calculating the inscribed square area.
Let x be the side length of the inscribed square.
a² = x²+(0.5x)²
a² = x²+¼(x²)
a² = ¼(5x²)
a = ½√(5)x units.
a is the radius of the circle.
b...
Calculating r, radius of the circle.
a² = 8²+24²-2*8*24cos60
a = 8√(7) cm.
b² = 6²+24²-2*6*24cos120
b = 6√(21) cm.
(24/sinc) = (8√(7)/sin60)
c = 79.1066053509°
d = 180-c
d = 100.893...
Calculating Shaded Area.
Let x be the radius of the inscribed circle.
a = (12+x) units.
a is the height of the ascribed right-angled triangle.
b = (18+x) units.
b is the base of the ascr...
Sir Mike Ambrose is the author of the question.
Calculating Area Orange, exactly in square cm.
Let AB be x.
Therefore BC = 2x cm.
Calculating x.
Yellow area + Area triangle with height...
Sir Mike Ambrose is the author of the question.
Calculating Blue Area.
Area blue exactly in cm² decimal form is;
Area trapezoid with two parallel sides 12 units and (12-16tan15) units, and h...
Calculating x, the last term of the series.
a = 7, first term.
d = 10-7 = 13-10 = 3, common difference.
S = 282, sum of the series.
It implies, calculating n, number of terms.
S = ½(n)(2...
Calculating Blue Area Total.
tana = 10/5
a = atan(2)°
b = 180-a
b = (180-atan(2))°
(10/sin(180-atan(2))) = (5/sinc)
c = 26.5650511771°
d = 180-(180-atan(2))-26.5650511771
d = 36.869...
Calculating the blue shaded area.
Let x be the radius of the half circle.
a = (x-2) cm.
Calculating x.
It implies;
x² = 4²+(x-2)²
x² = 16+x²-4x+4
4x = 20
x = 5 cm.
Again, x is t...
Sir Mike Ambrose is the author of the question.
Calculating Area Green ÷ Area Yellow to 3 d. p.
Let the side length of the regular pentagon be 2 units.
Therefore the angle theta is;
asin(...
Calculating x.
8 = 2³
It implies;
2^(3x)+2^(x) =130
Let 2^(x) = p.
p³+p = 130
130 = 1*2*5*13
It implies;
p = 5
Calculating x.
Recall.
p = 2^(x)
And p = 5
5 = 2...
