Let a be the radius of the inscribed circle.
b = ½(2a+1+4)
b = ½(2a+5) units.
b is the radius of the ascribed semi circle.
c = b-4
c = ½(2a+5)-4
c = ½(2a-3) units.
d = a-c
d = a-½(2a-...
Sir Mike Ambrose is the author of the question.
Let the side length of the ascribed square be 1 unit.
Area square is;
1²
= 1 square units.
a = ½(90-60)
a = 15°
tan15 = b/1
b = 0.267...
Sir Mike Ambrose is the author of the question.
Calculating k.
3k² = 108
k = 6 units.
The equation of the curve is;
y = 4x-⅓(x²)
Area R is;
Area under the curve at x=0 and x=(6-3√(2...
Sir Mike Ambrose is the author of the question.
Let the side of the regular quadrilateral (square) be 4 units.
Area square is;
4²
= 16 square units.
Area Red is;
Area triangle with he...
Let the radius of yellow circle be r.
Let the radius of the blue semi circle be R.
Calculating r.
(4r+1)x1=5x1
4r+1=5
4r = 4
r = 1 unit.
Calculating R.
2²+3²=R²
R = √(4+9)
R = √...
Calculating r, radius of the inscribed circle.
r²=(r-4)²+(r-2)²
r²=r²-8r+16+r²-4r+4
r²-12r+20=0
(r-6)²=-20+36
r = 6±√(16)
r = 6±4
Therefore;
r ≠ 2 units.
r = 10 units.
Therefore, area...
Area Blue (Star) is;
Area circle of radius 20 cm - 5(area triangle with two length 14.5308505601 cm and angle 108°, the angle they form) - 5(Area sector of radius 20 cm and angle 72°) + 5(area t...
Let CM be x.
Calculating x.
x+1 - x+3
1 - 2
Cross multiply.
2x+2=x+3
x = 1 units.
Therefore,
CM = 1 units.
Therefore angle C is;
Sin C = ½
C = 30°
Calculating AB.
N...
Sir Mike Ambrose is the author of the question.
Notice;
Side length of the congruent regular hexagon is 2 units.
(a) Calculating
Length Blue ÷ Length Red.
Length Blue is;
Let it be x....
Shaded red area is;
Area quarter of radius 10 units - Area sector of radius 10 units and angle 30° - Area equilateral triangle of single side length 5 units - Area sector of radius 5 units and a...
