Areca spp.
Common name: Palm tree, Palms
Cool climate palms
There are many different varieties of palms in Australia. Although palms are thought of as tropical trees there are now cool climate palms such as-

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Lady palm (Rhapis excelsa): These grow best in filtered light.
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Wedding palm (Lytocaryum weddellianum previously known as Microcoelum weddellianum): Grows best away from direct sunlight in humid, coastal areas and will take frost and exposure to sun.
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European fan palm (Chamaerops humilis): Best in sunny position and can tolerate cold down to -15°C.
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Dypsis baronni: this palm can survive to -6°C
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Walking stick palm (Linospadix monostachya): prefers a shady position in humid coastal areas. It will survive to -10°C.
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Bismarck palm (Bismarckia nobilis): Grows well in tropical areas and down to -6°C*
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Windmill palm (Trachycarpus fortunei): will tolerate either sun or shade

Warm climate palms

Bibliography:
http://www.burkesbackyard.com.au/1997/archives/27/in_the_garden/trees_and_palms/kentia_palms
http://www.burkesbackyard.com.au/1998/archive/26/in_the_garden/trees_and_palms/cool_climate_palms_and_ferns