what is the area of the rhombus? **Finding the Area of a Rhombus**In this lesson, we will learn how to find the area of a rhombus using its diagonals.### Given Information- One of the diagonals is 16 meters long.- The other diagonal is 12 meters long.### Diagram ExplanationThe provided diagram shows a rhombus with its diagonals intersecting at right angles. The diagonals are drawn as two perpendicular lines dividing the rhombus into four right-angled triangles.- The length of the vertical diagonal is marked as 16 meters.- The length of the horizontal diagonal is marked as 12 meters.### Formula for the Area of a RhombusThe area $ A $ of a rhombus can be calculated using the lengths of its diagonals $ d_1 $ and $ d_2 $ with the formula:\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]### CalculationSubstitute the given lengths of the diagonals into the formula:\[ \text{Area} = \frac{1}{2} \times 16 \, \text{m} \times 12 \, \text{m} \]### Final Area\[ \text{Area} = 96 \, \text{m}^2 \]### ConclusionThe area of the rhombus is $ 96 \, \text{m}^2 $.Feel free to use this formula to calculate the area of any rhombus if the lengths of its diagonals are known.

Answered: Find the area of the rhombus.

Math

Geometry

Find the area of the rhombus.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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what is the area of the rhombus?

**Finding the Area of a Rhombus**

In this lesson, we will learn how to find the area of a rhombus using its diagonals.

### Given Information
- One of the diagonals is 16 meters long.
- The other diagonal is 12 meters long.

### Diagram Explanation
The provided diagram shows a rhombus with its diagonals intersecting at right angles. The diagonals are drawn as two perpendicular lines dividing the rhombus into four right-angled triangles.

- The length of the vertical diagonal is marked as 16 meters.
- The length of the horizontal diagonal is marked as 12 meters.

### Formula for the Area of a Rhombus
The area $ A $ of a rhombus can be calculated using the lengths of its diagonals $ d_1 $ and $ d_2 $ with the formula:
\[ \text{Area} = \frac{1}{2} \times d_1 \times d_2 \]

### Calculation
Substitute the given lengths of the diagonals into the formula:
\[ \text{Area} = \frac{1}{2} \times 16 \, \text{m} \times 12 \, \text{m} \]

### Final Area
\[ \text{Area} = 96 \, \text{m}^2 \]

### Conclusion
The area of the rhombus is $ 96 \, \text{m}^2 $.

Feel free to use this formula to calculate the area of any rhombus if the lengths of its diagonals are known.

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