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 find out which diagonal measures cannot correspond to an area of \( 4 \, \mathrm{m}^2 \), we can use the formula for the area of a kite, given by: \[ \text{Area} = \frac{d_1 \cdot d_2}{2} \] By rearranging this formula, we can calculate the product \( d_1 \cdot d_2 \) that would give 8 (since \( 4 \times 2 = 8 \)). Let’s evaluate the options: 1. If \( d_1 = 2 \, m \) and \( d_2 = 2 \, m \): \[ \text{Area} = \frac{2 \times 2}{2} = 2 \, \mathrm{m}^2 \quad (\text{NOT } 4 \, \mathrm{m}^2) \] 2. If \( d_1 = 2.5 \, m \) and \( d_2 = 3.2 \, m \): \[ \text{Area} = \frac{2.5 \times 3.2}{2} = 4 \, \mathrm{m}^2 \quad (\text{VALID}) \] 3. If \( d_1 = 2 \, m \) and \( d_2 = 4 \, m \): \[ \text{Area} = \frac{2 \times 4}{2} = 4 \, \mathrm{m}^2 \quad (\text{VALID}) \] 4. Finally, if \( d_1 = 2 \, m \) and \( d_2 = 8 \, m \): \[ \text{Area} = \frac{2 \times 8}{2} = 8 \, \mathrm{m}^2 \quad (\text{NOT } 4 \, \mathrm{m}^2) \] Thus, the diagonal measures that cannot be used for the kite area of \( 4 \, \mathrm{m}^2 \) are \( d_1 = 2 \, m; d_2 = 2 \, m \) and \( d_1 = 2 \, m; d_2 = 8 \, m \).