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On Equator, why do objects cast the shortest shadows at 11:32 and not 12:00?

For instance, this happens in Costa Rica.

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    $\begingroup$ Because on the day you observed this, it wasn't the equinox. $\endgroup$ – zephyr Aug 24 '17 at 12:44
  • $\begingroup$ @zephyr while true, that falls into the category of "Microsoft Answer" $\endgroup$ – Carl Witthoft Aug 24 '17 at 13:25
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    $\begingroup$ @CarlWitthoft That's why it's only a comment. $\endgroup$ – zephyr Aug 24 '17 at 13:48
  • $\begingroup$ I've edited the question so that it reflects what I think the questioner meant. If not, I'm at a loss to understand what is being asked here at all! I would just add that Costa Rica isn't really all that close to the equator. $\endgroup$ – adrianmcmenamin Aug 25 '17 at 10:54
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If you look at the position of the sun at the same time each day, over the course of a year, you will find it traces a "figure of 8" pattern in the sky called an analemma. This may seem an extremely obscure thing to have a name, but it is important for sundial makers, and comes from sundial cant.

Now this means that the time that the sun will cross the meridian will vary from day to day. At the equator, the sun will travel directly overhead only on the equinoxes. In June, the sun will be in the North at midday, In December it will be in the South.

Each country is in a time-zone. It is a matter of convenience that the time in the country is all the same, rather than each location using their local solar time. At your location in Costa Rica you have found that solar noon occurs at 11:32. The Costa Rican's could choose to put their clocks forward an hour, but if they did, then local noon would be at 12:32.

The effect of time-zones is most extreme in the far west of China, where Beijing time is in use. There, local noon occurs at about 15:00. China chooses to have a single time zone, in contrast to other large countries like the USA or Russia.

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The time the sun is actually directly overhead depends on where you are in your time zone. In the eastern part of the time zone, the sun will be overhead sooner, and in the western part it will be overhead later. Where you are, it happens to be directly overhead at 11:32.

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    $\begingroup$ Yes, Costa Rica's timezone is GMT-6h, but its longitude is between 83 and 86W, thus "noon" occurs earlier than midday by roughly 12-28 minutes. However, the equation of time varies this by roughly +/- 15 minutes depending on the time of year. $\endgroup$ – Rob Jeffries Aug 24 '17 at 15:28

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