Calculating x, the length that form tangents of the two semi circles.
x²+2²=6²
x²=36-4
x²=32
x = √(32) cm.
x = 4√(2) cm.
Therefore;
Area blue is;
Area trapezium with two parallel le...
Shaded area is;
Area square with side 1542 units - Area equilateral triangle with side 1542 units - 2(area sector with radius 1542 units and angle 30°)
= 1542² - ½(1542)²sin60 - 2(30÷360*1542²...
Calculating R, radius of the bigger circle.
R²=(R-1)²+(R-2)²
R²-6R+5=0
Therefore;
R ≠ 1 units.
R = 5 units.
Its diameter is 10 units.
Calculating r, radius of the big circle.
It wil...
Calculating AB, the diameter of the circle.
Let it be x.
Sin(atan(⅓)) = √(6²+2²)/x
Sin(atan(⅓)) = √(40)/x
x = √(40)/sin(atan(⅓))
x = 20 cm.
x is AB.
Therefore length AC is;
AB - 2...
a = 180-100-50
a = 30°
(20/sin100) = (b/sin30)
b = 10.1542661189 cm
c = ½(180-100)
c = 40°
Let d be the radius of the circle.
tan40 = d/e
e = 1.1917535926d .
f = (10.1542661189-...
Total red area is;
3(area square with side 5 units - area quarter circle with radius 5 units) + Area triangle with height 5 units and base 10 units - Area sector with radius 5 units and angle 2a...
Sir Mike Ambrose is the author of the question.
Let the side length of the square be x.
Calculating x.
18²=x²+(x-6)²
324=x²+x²-12x+36
2x²-12x-288=0
x²-6x-144=0
(x-3)²=144+9
x = 3±√(153)...
Please, move the above question left/right one time to review the solution of the question.
Thank you.
Calculating x.
a = 4+1
a = 4 units.
a is the radius of the quarter circle.
b²+4² = 5²
b = √(25-16)
b = 3 units.
tanc = 3/4
c = atan(3/4)°
d = 90-c
d = atan(4/3)°
It implies;...
Sir Mike Ambrose is the author of the question.
Let the single side length of the inscribed regular pentagon be 2 units.
Therefore;
Area green is;
Area rectangle with length 2 units and w...
