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5 ft ーナ- 8 ft -H-----H--

5 ft ーナ- 8 ft -H-----H--

Elementary Geometry For College Students, 7e
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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Find the area of each trapezoid, rhombus, or kite.
**Geometry Problem: Rhombus** **Problem 4:** The diagram provided is of a rhombus with diagonals intersecting at right angles. Two highlighted measurements within the rhombus are: - One diagonal measuring 5 feet - The other diagonal measuring 8 feet The diagonals are annotated with dashed lines, indicating that they intersect at 90 degrees. The intersection point divides each diagonal into two equal segments, confirming that all sides of the rhombus are equal in length. **Explanation of Geometric Properties:** 1. **Diagonals of a Rhombus:** - The diagonals of a rhombus intersect at right angles (90 degrees). - They bisect each other, meaning each half of the diagonal creates two equal-length segments. 2. **Calculating the Area:** - The area \( A \) of a rhombus can be determined 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. Given: - \( d_1 = 5 \) feet - \( d_2 = 8 \) feet Step-by-step calculation: \[ A = \frac{1}{2} \times 5 \, \text{ft} \times 8 \, \text{ft} = \frac{1}{2} \times 40 \, \text{ft}^2 = 20 \, \text{ft}^2 \] **Conclusion:** The area of the rhombus in the diagram is 20 square feet. This geometric property highlights the significance of the lengths of the diagonals in determining the overall area of a rhombus.
Transcribed Image Text:**Geometry Problem: Rhombus** **Problem 4:** The diagram provided is of a rhombus with diagonals intersecting at right angles. Two highlighted measurements within the rhombus are: - One diagonal measuring 5 feet - The other diagonal measuring 8 feet The diagonals are annotated with dashed lines, indicating that they intersect at 90 degrees. The intersection point divides each diagonal into two equal segments, confirming that all sides of the rhombus are equal in length. **Explanation of Geometric Properties:** 1. **Diagonals of a Rhombus:** - The diagonals of a rhombus intersect at right angles (90 degrees). - They bisect each other, meaning each half of the diagonal creates two equal-length segments. 2. **Calculating the Area:** - The area \( A \) of a rhombus can be determined 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. Given: - \( d_1 = 5 \) feet - \( d_2 = 8 \) feet Step-by-step calculation: \[ A = \frac{1}{2} \times 5 \, \text{ft} \times 8 \, \text{ft} = \frac{1}{2} \times 40 \, \text{ft}^2 = 20 \, \text{ft}^2 \] **Conclusion:** The area of the rhombus in the diagram is 20 square feet. This geometric property highlights the significance of the lengths of the diagonals in determining the overall area of a rhombus.
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