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I calculated the polygon area through arcmap.but i'm not sure that the area is not actual,may be scale is not right.

so how to calculate the exact area of a jpg image?

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You can always use the draw tool (found in the draw toolbar). Draw a polygon around the image then double click it. It will show the area based on the units and coordinate system of the data frame.

You can also use the measure tool on the main toolbar that looks like a ruler -- it allows you to calculate area as well.

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Unless the .jpg is a .jp2 or has a coordinate system tagged to it, you cannot accurately measure the area. My recommendation is to check the coordinate system of your jpg. If there is no coordinate system and you cannot find the source info for the coordinate system (if applicable), then you should look toward Georeferencing. A fairly good source of information from ESRI can be found here:

Intro to Georeferencing

Georeferencing toolbar

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Do you know the resolution of the grid (=size of one pixel)? Then you are able to calculate the area: pixelsize x pixelsize x imageheight x imagewidth e.g. 2 meter x 2 meter x 3500 pixel x 4000 pixel = 56,000,000 squaremeter

(This only works if the image is stored in an equal area projection.)

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