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

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, which is given by: \[ \text{Area} = \frac{d_1 \times d_2}{2} \] Plugging in \(4 \, \text{m}^2\): \[ 4 = \frac{d_1 \times d_2}{2} \implies d_1 \times d_2 = 8 \] Now checking each set of diagonals: 1. \(d_1 = 2 \, \text{m}, d_2 = 2 \, \text{m} \implies 2 \times 2 = 4\) (not valid) 2. \(d_1 = 2.5 \, \text{m}, d_2 = 3.2 \, \text{m} \implies 2.5 \times 3.2 = 8\) (valid) 3. \(d_1 = 1 \, \text{m}, d_2 = 8 \, \text{m} \implies 1 \times 8 = 8\) (valid) 4. \(d_1 = 2 \, \text{m}, d_2 = 4 \, \text{m} \implies 2 \times 4 = 8\) (valid) The diagonal measures \(d_1 = 2 \, \text{m}\) and \(d_2 = 2 \, \text{m}\) cannot correspond to a kite with an area of \(4 \, \text{m}^2\) since they give an area of \(4 \, \text{m}^2\), not the required \(4 \, \text{m}^2\). So, that option doesn't hold given the area requirement. When kites were first flown in ancient China around 2000 years ago, they weren't just toys! These wonderful flying objects represented much more - they were used for military purposes, measuring distances, and even sending messages. Talk about a multi-functional marvel! If you’re inspired by kites, why not try making your own? You can cut out a diamond shape from a plastic bag or tissue paper, stick it on some wooden skewers, and attach a tail with ribbons. Customize it with colors and designs, then take it out on a breezy day! Watch it soar and feel the kite-flying joy firsthand!