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
Related questions
Question
![**Problem Statement:**
Find \( y \) if \( A = 51 \, \text{in}^2 \).
**Diagram Explanation:**
The diagram shows a trapezoid with one horizontal side labeled as 6 inches and the other as 12 inches. The height of the trapezoid, perpendicular to these two sides, is labeled \( y \).
**Calculation:**
The formula to calculate the area (A) of a trapezoid is:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
Where:
- \( A \) is the area
- \( b_1 \) and \( b_2 \) are the lengths of the parallel sides (6 in and 12 in)
- \( h \) is the height (\( y \))
Given:
\[ A = 51 \, \text{in}^2 \]
\[ b_1 = 6 \, \text{in} \]
\[ b_2 = 12 \, \text{in} \]
Substitute the known values into the formula:
\[ 51 = \frac{1}{2} \times (6 + 12) \times y \]
Solve for \( y \):
\[ 51 = \frac{1}{2} \times 18 \times y \]
\[ 51 = 9y \]
\[ y = \frac{51}{9} \]
\[ y = 5.67 \, \text{inches} \]
**Answer Input Field:**
\[ y = \, \_\_\_ \, \text{inches} \]
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Transcribed Image Text:**Problem Statement:**
Find \( y \) if \( A = 51 \, \text{in}^2 \).
**Diagram Explanation:**
The diagram shows a trapezoid with one horizontal side labeled as 6 inches and the other as 12 inches. The height of the trapezoid, perpendicular to these two sides, is labeled \( y \).
**Calculation:**
The formula to calculate the area (A) of a trapezoid is:
\[ A = \frac{1}{2} \times (b_1 + b_2) \times h \]
Where:
- \( A \) is the area
- \( b_1 \) and \( b_2 \) are the lengths of the parallel sides (6 in and 12 in)
- \( h \) is the height (\( y \))
Given:
\[ A = 51 \, \text{in}^2 \]
\[ b_1 = 6 \, \text{in} \]
\[ b_2 = 12 \, \text{in} \]
Substitute the known values into the formula:
\[ 51 = \frac{1}{2} \times (6 + 12) \times y \]
Solve for \( y \):
\[ 51 = \frac{1}{2} \times 18 \times y \]
\[ 51 = 9y \]
\[ y = \frac{51}{9} \]
\[ y = 5.67 \, \text{inches} \]
**Answer Input Field:**
\[ y = \, \_\_\_ \, \text{inches} \]
**Submit Question** (Button)
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