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

To determine which diagonal measures are **not** possible for 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 can set up the equation: \[ 4 = \frac{d_1 \times d_2}{2} \implies d_1 \times d_2 = 8 \] Now, let's evaluate each pair of diagonal measures: 1. **\(d_1 = 2 \, \text{m}; \, d_2 = 2 \, \text{m}\)** \[ d_1 \times d_2 = 2 \times 2 = 4 \neq 8 \] This pair **does not** satisfy the required product of 8, so it **cannot** be the diagonals of the kite. 2. **\(d_1 = 2.5 \, \text{m}; \, d_2 = 3.2 \, \text{m}\)** \[ d_1 \times d_2 = 2.5 \times 3.2 = 8 \quad (\text{Exactly 8}) \] This pair **does** satisfy the condition. 3. **\(d_2 = 8 \, \text{m}\)** Assuming \(d_1\) would need to be \(1 \, \text{m}\) to satisfy \(1 \times 8 = 8\), this pair is possible. 4. **\(d_1 = 2 \, \text{m}; \, d_2 = 4 \, \text{m}\)** \[ d_1 \times d_2 = 2 \times 4 = 8 \quad (\text{Exactly 8}) \] This pair **does** satisfy the condition. **Conclusion:** The diagonal measures \(d_1 = 2 \, \text{m}\) and \(d_2 = 2 \, \text{m}\) **cannot** form a kite with an area of \(4 \, \text{m}^2\). **Answer:** The pair with both diagonals equal to 2 m cannot be the kite’s diagonals.