# Thread: area of an "oval"

1. ## area of an "oval"

Hello

I want to calculate the area under the length "L" of this shape.
W, h and b are known.

I am using the formula for a ellipse, pi*h*L/4 but it is not so good when h gets bigger for instance or when b gets smaller.
When h is small, the calculated area with the elipse equation gets to big, and when h gets larger the calculated area get smaller than it really is..

Any ideas or tips ?

2. Originally Posted by danielel
Hello

I want to calculate the area under the length "L" of this shape.
W, h and b are known.

I am using the formula for a ellipse, pi*h*L/4 but it is not so good when h gets bigger for instance or when b gets smaller.
When h is small, the calculated area with the elipse equation gets to big, and when h gets larger the calculated area get smaller than it really is..

Any ideas or tips ?
"Under the length L"? Do you mean that the overall length of the figure is L and the height is h?
That figure can best be approximated by a rectangle with a half circle on
each end. In order that the half circle fit on the end of the rectangle its radius must be h/2. (In your picture there appears to be a small oddly region
between the rectangle and half circle that I am ignoring. That's why this is an approximation.) The area of the two half-circles together is $\pi r^2= \pi h^2/4$ and the area of the rectangle is hL. The area of the entire figure is approximately $hL+ \pi h^2/4$.

3. Sorry, the length L is just w-2b.
h is the height in the middle of the "oval".

4. Then replace my L by w- 2b. Again, since I have assumed a rectangular middle, that is only an approximation, how good the approximation is depends on there being very little change in the height for that part.

5. Yes, of course.

But what if the height does change and gets noticable smaller? is there any way to calculate the area under L then?