To find the area of a rhombus when given the lengths of its diagonals, we can use the formula:
[tex]\[
\text{Area} = \frac{1}{2} \times \text{Product of the lengths of the diagonals}
\][/tex]
Given:
- The length of the first diagonal ([tex]\(d_1\)[/tex]) is 3.5 centimeters.
- The length of the second diagonal ([tex]\(d_2\)[/tex]) is 5.0 centimeters.
Substituting these values into the formula, we get:
[tex]\[
\text{Area} = \frac{1}{2} \times (3.5 \times 5.0)
\][/tex]
First, calculate the product of the diagonals:
[tex]\[
3.5 \times 5.0 = 17.5
\][/tex]
Next, take half of this product to find the area of the rhombus:
[tex]\[
\text{Area} = \frac{1}{2} \times 17.5 = 8.75
\][/tex]
Therefore, the area of each rhombus-shaped piece is:
[tex]\[
8.75 \, \text{cm}^2
\][/tex]
Thus, the correct answer is:
[tex]\[
8.75 \, \text{cm}^2
\][/tex]
