Is this statement true or false?
The area of a rhombus can be found using the diagonals only if the side measure is
known.

Question

Is this statement true or false? The area of a rhombus can be found using the diagonals only if the side measure is known.

UpStudy AI · Accepted Answer

**False.**

The area of a rhombus can be calculated using the lengths of its diagonals without needing to know the length of its sides. The formula for the area $$ A $$ of a rhombus when the diagonals are known is:

$$
A = \frac{d_1 \times d_2}{2}
$$

where $$ d_1 $$ and $$ d_2 $$ are the lengths of the diagonals.

**Explanation:**

- **Rhombus Basics:** A rhombus is a quadrilateral with all four sides of equal length. Its diagonals intersect at right angles and bisect each other.

- **Area Formula Using Diagonals:** The formula $$ A = \frac{d_1 \times d_2}{2} $$ directly relates the area to the lengths of the two diagonals. This formula does not require any information about the side lengths of the rhombus.

- **No Need for Side Lengths:** Since the diagonals in a rhombus inherently relate to the vertex angles and intersect at right angles, knowing their lengths alone is sufficient to determine the area. The side lengths can be derived from the diagonals if needed, but they are not necessary for calculating the area.

**Example:**

Suppose a rhombus has diagonals of lengths 8 units and 6 units.

Using the area formula:
$$
A = \frac{8 \times 6}{2} = 24 \text{ square units}
$$

In this calculation, no information about the side lengths is required.

Therefore, the statement is **false** because knowing the side measure is not a prerequisite for finding the area using the diagonals.
The statement is false. You can find the area of a rhombus using its diagonals without knowing the side lengths.

Is this statement true or false?
The area of a rhombus can be found using the diagonals only if the side measure is
known.

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