You can take a photo of the leaf against a background with good contrast (a sheet of paper) with a ruler for scale in the image, and then you can calculate leaf area using ImageJ, as Briony mentioned. 

This video shows one relatively quick way of doing it (there are others)

https://www.youtube.com/watch?v=idsrN2NKtJ4

I hope that helps. 

If you are always studying the same species, you can do a calibration curve by measuring actual area, length and width of a leaf, and then you'll only have to measure length and with and enter them in the regression equation

Have a look at this website, where you can find software for image analysis of plant leaves, roots etc. Some of the programs are free (open source):

http://www.plant-image-analysis.org/

ImageJ (free) is highly recommended. very customisable and If you take all the pictures at the same focal distance you can batch process the whole lot quite quickly.

Existe una app para celulares con sistema operativo android que utiliza un cuadrado patron y en la cual se puede medir área foliar verde

https://play.google.com/store/apps/details?id=com.heaslon.EasyLeafArea&hl=es

I've developed an iOS app for measuring leaf surface area. See my project below.

https://www.researchgate.net/project/Leafscan-iOS-app-for-measuring-leaf-surface-area