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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa2a2b28e-9c88-4079-ae60-9bf329aa533a%2Ff95a01a9-6f13-45bb-a8ef-5eb6cf1002fa%2Fp2p5p8k_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**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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