# rectangle and circle question

**URL:** <https://boards.straightdope.com/t/rectangle-and-circle-question/108357>\
**Category:** Factual Questions\
**Created:** [May 10, 2002, 8:00pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357 "2002-05-10T20:00:24Z")\
**Posts on this page:** 7\
**Page:** 1

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**Author:** ![jb\_farley](https://avatars.discourse-cdn.com/v4/letter/j/9d8465/32.png) [@jb\_farley](https://boards.straightdope.com/u/jb_farley)\
**Post date:** [May 10, 2002, 8:00pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/1 "2002-05-10T20:00:24Z")

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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

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**Author:** ![Nametag](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/nametag/32/406_2.png) [@Nametag](https://boards.straightdope.com/u/Nametag)\
**Post date:** [May 10, 2002, 8:08pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/2 "2002-05-10T20:08:52Z")

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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.

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**Author:** ![DonJorge](https://avatars.discourse-cdn.com/v4/letter/d/47e85d/32.png) [@DonJorge](https://boards.straightdope.com/u/DonJorge)\
**Post date:** [May 10, 2002, 8:11pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/3 "2002-05-10T20:11:47Z")

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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.

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**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\
**Post date:** [May 10, 2002, 8:33pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/4 "2002-05-10T20:33:52Z")

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

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

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**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\
**Post date:** [May 12, 2002, 5:54pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/5 "2002-05-12T17:54:13Z")

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

Actually, it’s:

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

Sorry.

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**Author:** ![Bryan\_Ekers](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bryan_ekers/32/183_2.png) [@Bryan\_Ekers](https://boards.straightdope.com/u/Bryan_Ekers)\
**Post date:** [May 12, 2002, 6:51pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/6 "2002-05-12T18:51:48Z")

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Or, expressed more simply:

pi(a² + b²)/4

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**Author:** ![KneadToKnow](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kneadtoknow/32/3999_2.png) [@KneadToKnow](https://boards.straightdope.com/u/KneadToKnow)\
**Post date:** [May 12, 2002, 7:00pm UTC](https://boards.straightdope.com/t/rectangle-and-circle-question/108357/7 "2002-05-12T19:00:20Z")

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