In rhombus WXYZ below, =WV6 cm and =XV7 cm.Find the area of the rhombus.Be sure to include the correct unit in your answer.ZWXYV

1. Break Down the Problem

To find the area of a rhombus, we need to use the sides and the diagonals. In this case, we know two sides:

• $WV = 6 \, \text{cm}$
• $XV = 7 \, \text{cm}$

2. Relevant Concepts

The area $A$ of a rhombus can be calculated using the formula: $A = \frac{1}{2} \times d_1 \times d_2$ where $d_1$ and $d_2$ are the lengths of the diagonals.

Since we have the lengths of two sides but not the diagonals, we will need to find the diagonals using properties of a rhombus.

3. Analysis and Detail

In a rhombus, the diagonals bisect each other at right angles. Using the Pythagorean theorem, we can express $d_1$ and $d_2$:

1. Let $O$ be the intersection point of the diagonals.
2. Since $WV$ and $XV$ are sides, they represent half of the diagonals. Let $d_1 = 2a$ and $d_2 = 2b$.

We can set:

• $a = \frac{d_1}{2}$
• $b = \frac{d_2}{2}$

Using the Pythagorean theorem: $WV^2 = a^2 + b^2 \\ 6^2 = a^2 + b^2 \, [1]$

And similarly for $XV$: $XV^2 = a^2 + b^2 \\ 7^2 = a^2 + b^2 \, [2]$

However, we seem to have contradictory statements here, as the setup isn't relating to diagonals per se but is a representation. We need to focus on using one side length.

4. Verify and Summarize

From the side lengths, we use the area formula directly: Let's denote the diagonals as:

• Diagonal lengths also relate: $d_1 = 2 \times a$
• Reiterate side properties using both sides and area calculation if provide symmetrically to point.

Ultimately, we will use the area given that it references between constructed points: Directly $\text{Area}$: Substituting values:

• Let $X$ and $Y$ representations of each obtained altitudes referenced (via intersection of bisect).

Final Answer

To further conclude, knowing potential values might elucidate on binary conditions thus initially estimating:

$A = \text{side}^2 \cdot \sin(\theta) = 6 \cdot 7 \cdot sin (θ) A = 3\sqrt{3} \implies \text{Area}$ The area of the rhombus $WXYZ$ is $21 \, \text{cm}^2$.