In The BFG, UK helicopters carry giants and leave them on an island:
Are helicopters capable of carrying this type of giants?
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There are basically two models of helicopter in this image.
The Sikorsky CH-54 is capable of carrying a payload of 20,000 pounds i.e 9000 Kg while a CH-47 Chinook can carry up to 10,000 pounds i.e 4500 Kg.
Now guessing from size of those giants they might vary from 3000 to 6000 kg.
Calculating weight of giants.
The height of each man-eating giant is around 50 feet (15 metres), according to Wikipedia. And from the their body mass I will consider them obese which means they have a BMI ranging from 25 to 30.
So BMI = Weight in KG / (Height in Metres)^2
Hence, Weight = BMI * (Height)^2
Assuming BMI = 25, Weight = 25 x 15 x 15 = 5625 Kg which is close to 6000 Kg.
Assuming BMI = 30, Weight = 30 x 15 x 15 = 6750 Kg which is close to 7000 Kg.
So the calculated weight ranges from 6000 to 7000 Kg. Right below the payload limit.
So yes, those helicopters can carry those giants.
Transport helicopters are capable of carrying quite heavy and cumbersome loads externally as sling-load or underslung cargo, as long as the external load is properly attached and balanced and its weight doesn't exceed the max. permitted weight limit.
One of the helicopters in the picture is a Sikorsky CH-54 Tarhe (S-64 Skycrane) which is purposefully built to transport heavy, extreme loads. It can carry a jet fighter, or a house as underslung cargo, as pictured below:
And here is a Tarhe carrying a Chinook helicopter as underslung cargo:
So the way they carry the giants is realistic, this method of external load transport by helicopters is not uncommon in real life. If the giant's weight is within the max. premitted weight limits, then it is OK to transport them this way. But, after all, this is a movie, and in the world of movies everything is possible. The way the helicopters transport the giants in The BFG is certainly much more realistic than the way the jaegers are transported in Pacific Rim:
This will never happen in real life.
I took easier approach than calculating mass. I took some info about similar sized animals. See info about Humpback Whale:
Adult males measure up to a maximum length of 15 – 18m and weight of 40 tonne. Adult females measure up to 15m and weigh from 22 to 35 tonne.
This is way over the limit as indicated by other posts.
As I said in a comment, this is completely unrealistic (which is not surprising and not bad; it's a fantasy movie!).
As an approximation, the giants roughly look the size of the helicopters. For an estimate let's assume block shape of the helicopter's dimensions, 27x7x7m, or 1323 m3, meaning >1000 metric tons of mass, assuming the usual body density of about 1. That's roughly 100 times the payload of a sky crane. If we mis-estimated by a linear factor of 2 (which would be a little less than the size the giants have in the book, 50 ft) the weight would still be 1323/2^3 = 165 tons, 16 times the payload. (But actually the guy in the front looks significantly larger than the copter carrying him.)