how do you go about finding out the area of an oval shaped flat object?

Question

this will be interesting

Answer 1

Ellipse area =
(pi) x (length of longest radius) x (length of shortest radius.)

If your oval is not an ellipsoid, but is more closely approximated in shape by a parabolic curve, then,
area =
8/3 (length of longest radius) x (length of shortest radius)

If you don't need a precise answer, and can't be sure of the oval shape for a formula, another good way is to just get some quarter inch graph paper, lay it on top, trace it out, and count the little squares. If it's quarter inch graphy paper, each one is a quarter inch x quarter inch, meaning the area of each square will be 1/16 of a square inch. Add up all the ones that are cut in half along the edge too. Just use half the area for each one, and it will average out.

- Kevin

Answer 2

The area of an ellipsoid involves elliptical integrals, which have no exact answer in terms of ordinary functions, but in terms of elliptic functions. See link. In the special cases of either problate or oblate spheroids, the solution is a bit easier. See 2nd link.

If you have an arbitrary "oval flat object", and if it can be scanned to form a 3D object in the computer, there are software that can give a numerical approximation of its area. There are even software that can "reconstruct" the 3D shape of the object based on photographs of it taken from a number of different angles, with accuracy increasing with the number of them.

A desperate bone-headed way to do it would be to grease it slightly, and then completely cover it with tiny ball bearings of uniform size, and then count them. A very good estimate can be found by this means, after factoring in packing densities of spheres and that it's an envelope. Still another way, an "on the fleld method", is to stick cut pieces of masking tape on it so that there are no overlapping nor gaps nor wrinkling. Then lay the bits of tape flat on a surface somewhere and carefully add up the areas.

Addendum: Read TheWhiz's answer below for a FLAT 2D "oval". Sheesh! Yeah, go weigh the paper.

Answer 3

If it's really an ellipse (a true oval) not an egg-shape, then its area may be calculated by determining the length of half the major and half the minor axis (the equivalents of the radius in a circle), let's call 'em p and q, and determining the product pi*p*q.

If you DON'T know the exact shape, I'd use the same method I'd use for figuring out the area of any irregular object: approximate by breaking it up into shapes I can figure out. This'd take some creativity - maybe break it up into triangles. If you have a sensitive balance and some nice paper, you could determine the density of your paper (mass/cm2), cut out a matching shape, and weigh the paper to find the area.

Answer 4

Most non-geeks confuse an oval with an ellipse and vice versa. I'll give both solutions and a third technique that works for any irregularly shaped 2-dimensional shape.

OVAL: Multiply the length of the straight section by the width of the straight section. Save this result and call it "rectangle." Next, take the width of the straight section and divide it by two. This is the radius of the two half-circles at each end. Square this radius and multiply by pi (3.14159). Save this result and call it "circle." Lastly, add "rectangle" and "circle." This is the total area of the measured oval.

ELLIPSE: Measure the overall length and divide it by two. Save this result as "major." Measure the maximum width and divide it by two. Save this result as "minor." The area of the ellipse is found by multiplying "major" times "minor" times "pi."

ANY SHAPE: Begin with a rectangular sheet of paper that's larger than the object you wish to measure. Measure the paper and multiply length times width. Save this value as "rectangle." Now carefully fold the paper and weigh it on a triple-beam balance with the greatest accuracy you can manage. Divide the area of "rectangle" by the weight. Save this value as "constant." Next, spread the paper over the object you wish to measure. Carefully trace the outline of the object and use scissors to trim the paper exactly to the outline. Fold the pattern and weigh it on the triple-beam. Save this value as "pattern." The area of the irregular shape is equal to "constant" times "pattern."