I was doing a simple geometry research a long time ago, but I got stuck on a problem. I have asked and searched, but I have not found an answer to it for a very long time.
If anyone could help me I would be very grateful.

I know that A=p×a×b
My question is:

What is the Area of an ellipse when a=0.5 and b=unknown

Thanks so much

It depends on b...
A can get almost any value....


Yatir

is there a formula to find b by using the circumference?

A=p×a×b

if A=p/2 and a=0.5 then:

p/2=p×1/2×b

and therefore b=1
Yatir

Yatir, E.C. wanted the circumference, not the area, to be pi/2.

I believe that this is actually impossible to solve in simple form. The circumference of an ellipse is very, very difficult to calculate.

David

oops I didn't see that...

I checked in a formulae list and
The perimeter of an ellipse is given by:

Which is very hard to calculate.
But they also gave an approximation:
Perimeter

=2p

_________ Ö1/2(a2+b2)

Yatir

For more on the circumference of an ellipse, see here in Asked NRICH.
If anyone reading doesn't know about the area of an ellipse, the formula and some ways of finding it are here .

Thanks so much for the suggestions and the links, I will try using them.