Posted by **alysa** on Monday, January 21, 2013 at 2:29am.

the perimeter of an ellipse with an area equal to 12pi square units if the non opposite vertices are 5units apart

- solid mensuration -
**bobpursley**, Monday, January 21, 2013 at 5:01am
http://www.mathwarehouse.com/ellipse/area-of-ellipse.php

- solid mensuration -
**Reiny**, Monday, January 21, 2013 at 10:00am
What a nasty question.

the area of the ellipse is abπ , where a and b are each 1/2 of the axes

so abπ = 12π --->ab = 6 or b = 6/a

let A(a,0) and B(0,b) be the two adjacent vertices

given AB = 5

√(a^2 + b^2) = 5

a^2 + b^2 = 25

a^2 + 36/a^2 = 25

a^4 + 36 = 25a^2

a^4 - 25a^2 + 36 = 0

a^2 = (25 ± √481)/2 = appr 23.4658 or appr 1.53414

a = 4.844157.. or a = 1.2386... ignoring the 2 negative values

then b = 6/a

if a = 4.844148, then b = 1.2386

if a = 1.2386 , then a = 4.844157

ahhh, summetrical answers

So we basically have the same ellipse, one horizontal, one vertical

The perimeter of an ellipse is one of the most challenging questions dealing with the ellipse.

It requires Calculus and finding the length of a curve.

Here is a link that has some approximation methods

http://www.mathsisfun.com/geometry/ellipse-perimeter.html

Here is an applet that let's you find all properties of an ellipse

http://www.cleavebooks.co.uk/scol/callipse.htm

enter the 2a= 9.6883

enter 2b = 2.47721..

and press calculate to get a perimeter of appr. 20.87

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