The key here is to realize that the world price is going to hit the (domestic) demand curve further along than it hits the supply curve; that difference is the amount imported. It actually looks a lot like a price ceiling on the graph, only that gap isn't deadweight loss from transactions that don't happen; it's now gains from trade.
Thanks for giving me the demand function. I've graphed it in blue.
We aren't given the supply curve, but we can infer it because we're told that it is linear. Initially we are selling 30 units at $10; after opening trade we are selling 15 units at $5. So the supply curve must be the line that connects those two points, which is just P = 1/3Q. (I've drawn that in red.)
Once we open trade, we add a line for the world price of $5, which like I said acts a bit like a price ceiling. (I've drawn that in green.)
Now we add a tariff of $2, which effectively raises the world price to $7. (I've drawn that in a lighter green.) Notice how the total quantity purchased (where $7 intersects the demand curve) has decreased to 36 units instead of 40 units.
Domestic production has risen, to where $7 intersects the supply curve, at 21 units. Imports have therefore fallen, from 25 units to 15 units. (Vertical lines in orange show these cutoffs.)
This does make the domestic suppliers better off; their producer surplus rises by the (trapezoidal) segment to the left of the supply curve. It reduces the consumer surplus by the total (trapezoidal) segment to the right of the supply curve. It raises revenue for the government, but only on the 15 units actually sold, a rectangular segment which is $2 by 15 units.
As a result, there is a deadweight loss segment, which is two triangles (shaded in orange). Each has a height of $7-$2. One has a width of 40-36 = 4 units, while the other has a width of 21-15 = 6 units.Thus the total deadweight loss is the area of those two triangles, 1/2($2)(4) + 1/2($2)(6) = $10. Therefore choice C is correct.
In general, if the government could find a way to redistribute income from the buyers to the sellers without the tariff, and with no other market distortions, they could achieve a Pareto improvement relative to the tariff.