rectangle and circle question

Factual Questions
1

hello.

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,

jb

2

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.

3

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.

4

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

Area=pi(a^2+b^2)

5

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

Actually, it’s:

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

Sorry.

6

Or, expressed more simply:

pi(a² + b²)/4

7

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