To determine the area of a rhombus when you know the lengths of its diagonals, you can use the following formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{diagonal1} \times \text{diagonal2} \][/tex]
where [tex]\(\text{diagonal1}\)[/tex] and [tex]\(\text{diagonal2}\)[/tex] are the lengths of the diagonals.
Given:
- Diagonal 1 ([tex]\(\text{d}_1\)[/tex]) = 7 inches
- Diagonal 2 ([tex]\(\text{d}_2\)[/tex]) = 5 inches
Let's plug these values into the formula:
[tex]\[ \text{Area} = \frac{1}{2} \times \text{d}_1 \times \text{d}_2 \][/tex]
[tex]\[ \text{Area} = \frac{1}{2} \times 7 \times 5 \][/tex]
[tex]\[ \text{Area} = \frac{1}{2} \times 35 \][/tex]
[tex]\[ \text{Area} = 17.5 \][/tex]
Therefore, the area of the rhombus is:
[tex]\[ \text{Area} = 17.5 \, \text{in}^2 \][/tex]
So the correct answer is:
[tex]\[ 17.5 \, \text{in}^2 \][/tex]
