A kite has an area of $$ 4 \mathrm{~m}^{2} $$. Which of the following cannot be diagonal measures for this kite? $$ d_{1}=2 \mathrm{~m} ; d_{2}=2 \mathrm{~m} $$ $$ d_{1}=2.5 \mathrm{~m} ; d_{2}=3.2 \mathrm{~m} $$ $$ d_{1}=1 \mathrm{~m} ; d_{2}=8 \mathrm{~m} $$ $$ d_{1}=2 \mathrm{~m} ; d_{2}=4 \mathrm{~m} $$

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To determine which set of diagonal measures cannot correspond to a kite with an area of $$4 \, \text{m}^2$$, we can use the formula for the area of a kite:

$$
\text{Area} = \frac{d_1 \times d_2}{2}
$$

Given that the area is $$4 \, \text{m}^2$$, we have:

$$
\frac{d_1 \times d_2}{2} = 4 \implies d_1 \times d_2 = 8
$$

Now, let's evaluate each option:

1. **$$d_1 = 2 \, \text{m}; \, d_2 = 2 \, \text{m}$$**
   $$
   2 \times 2 = 4 \neq 8
   $$
   This does **not** satisfy the required product of 8.

2. **$$d_1 = 2.5 \, \text{m}; \, d_2 = 3.2 \, \text{m}$$**
   $$
   2.5 \times 3.2 = 8
   $$
   This satisfies the condition.

3. **$$d_1 = 1 \, \text{m}; \, d_2 = 8 \, \text{m}$$**
   $$
   1 \times 8 = 8
   $$
   This satisfies the condition.

4. **$$d_1 = 2 \, \text{m}; \, d_2 = 4 \, \text{m}$$**
   $$
   2 \times 4 = 8
   $$
   This satisfies the condition.

**Conclusion:** The diagonal measures $$d_1 = 2 \, \text{m}$$ and $$d_2 = 2 \, \text{m}$$ do not satisfy the area requirement of $$4 \, \text{m}^2$$ because their product is only 4, not 8.

**Answer:** 
A kite with diagonals both equal to 2 m cannot have an area of four square meters.
Diagonals of 2 m each cannot form a kite with an area of 4 m².

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