An artist makes a hanging sculpture out of rhombus-shaped pieces. Each rhombus shape has diagonals of 3.5 centimeters and 5 centimeters. What is the area of each rhombus?

A. [tex]4.25 \, \text{cm}^2[/tex]
B. [tex]8.5 \, \text{cm}^2[/tex]
C. [tex]8.75 \, \text{cm}^2[/tex]
D. [tex]17.5 \, \text{cm}^2[/tex]



Answer :

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]