Question

what is the estimated perimeter of an ellipse if the axis has a length of 15 feet and the minor axis has a length of 7.5 feet​

Answer 1

Ellipse perimeter = PI*(3*(a+b) -sqrt (10*a*b + 3*(a^2 + b^2)) (See Attached)

where a = semi-major axis and b = semi-minor axis

a = 15/2 = 7.5 and b = 7.5/2 = 3.75

Ellipse perimeter = PI * (3 * (7.5 + 3.75) - sqrt( 10 * 7.5 * 3.75) + 3 * (7.5^2 + 3.75^2)

Ellipse perimeter = PI * (33.75 - sqrt[( 281.25 + 3* (56.25 + 14.0625 )]

Ellipse perimeter = PI * (33.75 - sqrt(281.25 + 210.9375 )

Ellipse perimeter = PI * (33.75 - sqrt (492.1875 )

Ellipse perimeter = PI * (33.75 -22.1852991866 )

Ellipse perimeter = PI * 11.5647008134

Ellipse perimeter = 3.1415926536 * 11.5647008134

Ellipse perimeter = 36.3315791163

or Ellipse perimeter = 36.33 feet (rounded)

Explanation: