Area of an OvalDate: 11/30/2001 at 17:32:40 From: Colin Franks Subject: Area of an Oval How do I figure out the AREA of an oval? The oval in question is 17" x 38" and I need to know the total square feet. Or, more specifically, how much bigger (proportionally) I can make this oval to achieve 4.3 sq. ft. Thank you. Colin Date: 11/30/2001 at 19:15:06 From: Doctor Paul Subject: Re: Area of an Oval In mathematics, an "oval" is more correctly called an ellipse, and the area of an ellipse is given by Pi*a*b, where 2*a is the length of the longer side (measured at its greatest width) and 2*b is the length of the shortest side (measured at its greatest height). Here's a picture of how to measure, from Eric Weisstein's World of Mathematics:: Ellipse http://mathworld.wolfram.com/Ellipse.html In your case, we have a = 19 inches and b = 8.5 inches. Since you want the area to be in square feet, let's do the conversion: a = 19/12 feet and b = 8.5/12 feet Thus the area of this ellipse is Pi*19*8.5/144 = 3.52 square feet. That's not what you need, though, since we need to somehow expand a and b while keeping the relation: a/b = 38/17 This says that a = 38*b/17 Using this formula, we want the area to be 4.3 sq feet, so Pi*a*b = 4.3 Substituting for a gives: Pi*(38*b/17)*b = 4.3 so that says: b^2 = 4.3*17/(38*Pi) = .61233 ft b = .7825 ft = 9.39 inches plugging in b = 9.39 in the formula a = 38*b/17 gives a = 20.9898 inches Thus the dimensions of your oval should be 9.39*2 x 20.9898*2 or 18.78 inches x 41.98 inches I hope this helps. Please write back if you'd like to talk about this some more. - Doctor Paul, The Math Forum http://mathforum.org/dr.math/ |
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