Friday

April 18, 2014

April 18, 2014

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

- solid mensuration -
**bobpursley**, Monday, January 21, 2013 at 5:01am - solid mensuration -
**Reiny**, Monday, January 21, 2013 at 10:00amWhat 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

**Related Questions**

geometry - The area of an ellipse in the form (x*x/a*a)+(y*y)/(b*b)=1 is A=3.14*...

Calculus - I seriously do not understand anything about this problem Please ...

solid mensuration - A circle has an area equal to 25 pi sq.cm. Its diameter AB ...

solid mensuration - what is the area of a parabola inscribed in a rectangle 30cm...

solid mensuration - find the area of a regular pentagram if one of the sides of ...

solid mensuration - Find the area of a portion of a semicircle of radius 15 m ...

solid mensuration - what is the area of a section bounded by a closed elliptical...

solid mensuration - The base of a right prism is a rhombus whose sides are 20cm ...

solid mensuration - What is the area of a section bounded by a closed elliptical...

solid mensuration - circle c has radius of 10 cm. each of the points B and D is ...