Please, move the above question left/right one time to review the solution.
Thank you.
Sir Mike Ambrose is the author of the question.
Please, move the above question left/right one time to review the solution.
Thank you.
1²+(1-x)²=(1+x)²
1+1-2x+x²=1+2x+x²
1 = 4x
x = ¼ units.
Therefore;
Area Orange/Shaded is;
Area triangle with height 1 unit and base (1-x) units.
= ½(1*(1-x)), and x = ¼ units.
= ½(1-...
a = (24-R) units.
It implies;
R² = (24-R)²+12²
R² = 576-48R+R²+144
48R = 576+144
48R = 720
4R = 60
R = 15 units.
Calculating x, side length of the inscribed regular hexagon.
sin60 = a/6
2a = 6√(3)
a = 3√(3) units.
It implies;
Calculating x.
(2x)² = 6²+(3√(3))²
4x² = 36+27
4x² = 63
x² = 63/4...
Let the square side be 3 units.
Area of the plane shape is;
Area square with side 3 units + Area triangle with height 3 units and base ½(3) units.
= 3²+(½*½(3)*3)
= 9+(9/4)
= 45/4 space...
Sir Mike Ambrose is the author of the question.
Let the side length of the inscribed square be 1 unit.
Therefore;
Area square is;
1²
= 1 space units.
Area turquoise is;
Area triang...
Let the side length of the ascribed pentagon be 1 unit.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the regular pentagon.
b = ½(a)
b = 54°
cos54 = c/1
c = 0.5877852523 un...
Let the side length of the hexagon be 2 units.
a = ⅙*180(6-2)
a = 120°
b = ½(360-(30+90))
b = ½(240)
b = 120°
(2/sin45) = (c/sin15)
c = 0.7320508076 units.
Calculating Area Blue....
Calculating Length AB.
cosa = 5/6
a = acos(5/6)°
b = 90-a
b = (90-acos(5/6))°
Therefore, the required length, AB is;
cos(90-acos(5/6)) = 2/c
Where c is AB.
c = 2/cos(90-acos(5/6))
c...
