rectangle and circle question


given a rectangle of height a and length b, is it possible to derive the area of a circle, a circle which contains all four corners of the rectangle as points on its line?

if so, how?

thank you,


Easily. If you set the origin of two axes at the center of the rectangle, the corner of the rectangle represents a point with coordinates (b/2, a/2). The distance from the origin to the corner of the rectangle is also the radius ® of the circle: r^2 = (b/2)^2 + (a/2)^2.

The area of a circle is pi times r^2.

This looks like a circle with centre in the middle point of the rectangle, and radius equal to half the length of the diagonal.
The radius r of such circle will be the half the square root of a^2 + b^2, and it’s area can be calculated by the standard formula pi*r^2.

Or, for the plug-in-the-numbers all in one step answer:


I screwed that up and it’s been bothering me all weekend!

Actually, it’s:

pi( (sqrrt(a^2 + b^2)) / 2 )^2


Or, expressed more simply:

pi(a² + b²)/4

Dang. Do I have to turn in my diploma now? :wink: