Okay, let's tackle this problem step by step. So, we have a square, and two of its opposite sides are decreased by 40%, while the other two sides are increased by 50%. After these changes, it becomes a rectangle. The question is asking by what percent the square's area decreases. Hmm, let me think.

First, let me recall that the area of a square is side length squared. If we change the sides, we need to figure out the new area and compare it to the original area. The problem mentions decreasing two opposite sides by 40% and increasing the other two by 50%. Since a square has all sides equal, but here we're modifying two pairs of sides. So, the resulting figure is a rectangle with two sides shorter and two sides longer.

Let me denote the original side length of the square as 's'. Then, the original area is s².

Now, decreasing two opposite sides by 40% would mean that each of those sides becomes 60% of the original length. So, 0.6s. Similarly, increasing the other two sides by 50% would make them 1.5s each.

Wait, hold on. So, if the original square has sides all of length 's', then after modification, the rectangle would have sides of length 0.6s and 1.5s. Since a rectangle has length and width, the area would be length multiplied by width. Therefore, the new area would be 0.6s * 1.5s. Let me compute that.

0.6 times 1.5 is... 0.6 * 1.5. Let me calculate that. 0.6 * 1 = 0.6, 0.6 * 0.5 = 0.3. So, 0.6 + 0.3 = 0.9. Therefore, 0.9s². So the new area is 0.9 times the original area. Therefore, the area has decreased by 10%. Wait, that seems straightforward, but let me check again.

Original area: s². New area: (0.6s)(1.5s) = 0.9s². So, the area is 90% of the original, which means a 10% decrease. Hmm, but let me confirm if this is correct because sometimes when you change the sides, the effect might not be as straightforward.

Wait, but in a square, all sides are equal, so when you change two opposite sides, those sides become 0.6s, and the other two sides become 1.5s. Since a rectangle has two different side lengths, the area is indeed the product of the two different side lengths. So, multiplying 0.6s by 1.5s gives 0.9s². Therefore, the area is 90% of the original, so a 10% decrease. That seems right.

But let me think again. Maybe there's a different way to approach this problem. Let's consider the original square with side length 's'. If we take two sides and decrease them by 40%, that's 0.6s each, and the other two sides are increased by 50%, which is 1.5s each. So, the rectangle's dimensions are 0.6s by 1.5s. Area is 0.6 * 1.5 = 0.9, so 90% of the original area. Therefore, a 10% decrease. So, the answer would be 10%.

Wait, but maybe the problem is in the way the sides are changed. The problem says "the lengths of two opposite sides of a square are decreased by 40% while the lengths of the other two sides are increased by 50%". So, in a square, opposite sides are equal. So, if we decrease two opposite sides by 40%, those two sides become 0.6s each. Then the other two sides, which are opposite to each other, are increased by 50%, so 1.5s each. So, yes, the rectangle would have sides 0.6s and 1.5s. Therefore, area is 0.6 * 1.5 = 0.9. So, 10% decrease.

Alternatively, maybe there's a different interpretation. For example, maybe the problem is referring to modifying the square into a rectangle where two sides are decreased by 40% and the other two sides are increased by 50%. But in that case, the sides being decreased and increased are all sides, so opposite sides. But in a square, all sides are equal, so decreasing two opposite sides would mean those sides are 0.6s, and increasing the other two would mean those sides are 1.5s. So, the rectangle would have dimensions 0.6s and 1.5s. Therefore, the area is 0.9s², which is 90% of the original. So, the area decreases by 10%.

Alternatively, maybe the problem is referring to the sides as length and width, but in a square, length and width are the same. Wait, but in a square, all sides are equal, so when you decrease two opposite sides by 40% and increase the other two by 50%, you're effectively turning the square into a rectangle with different side lengths.

Wait, but in a square, all sides are equal, so modifying opposite sides would mean that the sides that are being decreased are opposite to each other, and the sides that are being increased are opposite to each other. Therefore, the resulting rectangle would have two sides of 0.6s and two sides of 1.5s. Therefore, the area is 0.6s * 1.5s = 0.9s². So, 10% decrease.

But let me check with numbers. Suppose the original square has side length 10 units. Then the original area is 100 square units. If we decrease two opposite sides by 40%, each of those sides becomes 6 units (40% decrease from 10). The other two sides are increased by 50%, so each becomes 15 units. Then the area is 6 * 15 = 90 square units. The original area was 100, so the decrease is 10 square units, which is 10% of the original area. Therefore, 10% decrease.

Therefore, the answer is 10%. So, the square's area decreases by 10%.

Wait, but let me make sure I didn't make a mistake here. Sometimes when you have percentage increases and decreases, it's easy to get tripped up. For example, if you have a 40% decrease and a 50% increase, the overall effect isn't a 10% decrease, but in this case, since we're dealing with two sides, it's multiplicative. So, 0.6 * 1.5 = 0.9, which is 90%, so 10% decrease. So, yes, that seems correct.

Alternatively, maybe the problem is referring to the change in area in terms of absolute numbers. For example, if the original area is A, then the new area is 0.6 * 1.5 * A = 0.9A. Therefore, the area decreases by 0.1A, which is 10% of the original area. So, the percentage decrease is 10%.

Therefore, the answer should be 10%. Hmm, seems straightforward. Wait, but let me think again. Suppose the original square has side length 1. Then original area is 1. After changing, the area is 0.6 * 1.5 = 0.9. So, 0.9 is 90% of 1. So, 10% decrease. So, yes, that's correct.

Alternatively, maybe the problem is trying to trick me into thinking about the perimeter or something else, but no, the question is about the area. So, the perimeter isn't involved here. It's just about the sides being modified and the area computed accordingly.

Therefore, I think the answer is 10%. So, the square's area decreases by 10%.
Therefore, the square's area decreases by $\boxed{10\%}$.
</think>