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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Question
![### Understanding the Area of a Triangle
Below is an image of a triangle with dimensions:
- The height of the triangle is labeled as 7 km.
- The base of the triangle is labeled as 5.4 km.
Additionally, the image includes a right-angled triangle drawn within the main triangle, indicated by a red dashed line. This red dashed line represents the height from the vertex perpendicular to the base of the triangle.
### Calculation of the Area
To find the area of a triangle, use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Based on the given triangle:
- Base (\( b \)): 5.4 km
- Height (\( h \)): 7 km
Now, substitute these values into the formula:
\[ \text{Area} = \frac{1}{2} \times 5.4 \, \text{km} \times 7 \, \text{km} \]
\[ \text{Area} = \frac{1}{2} \times 37.8 \, \text{km}^2 \]
\[ \text{Area} = 18.9 \, \text{km}^2 \]
Therefore, the area of the triangle is 18.9 square kilometers.
Please complete the blank in the image accordingly:
\[ \text{area is } 18.9 \, \text{km}^2 \] (don't round)
### Summary
Graphically, the triangle and the calculations demonstrate how to determine the area of a triangular shape using its base and height. Understanding this concept is fundamental in geometry and can be applied to various practical and theoretical problems.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc797aff8-bf05-4e13-9797-dfba08dadef9%2F818a9923-3a6f-4d64-af05-54c8d50e5007%2F07gxpen_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding the Area of a Triangle
Below is an image of a triangle with dimensions:
- The height of the triangle is labeled as 7 km.
- The base of the triangle is labeled as 5.4 km.
Additionally, the image includes a right-angled triangle drawn within the main triangle, indicated by a red dashed line. This red dashed line represents the height from the vertex perpendicular to the base of the triangle.
### Calculation of the Area
To find the area of a triangle, use the formula:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
Based on the given triangle:
- Base (\( b \)): 5.4 km
- Height (\( h \)): 7 km
Now, substitute these values into the formula:
\[ \text{Area} = \frac{1}{2} \times 5.4 \, \text{km} \times 7 \, \text{km} \]
\[ \text{Area} = \frac{1}{2} \times 37.8 \, \text{km}^2 \]
\[ \text{Area} = 18.9 \, \text{km}^2 \]
Therefore, the area of the triangle is 18.9 square kilometers.
Please complete the blank in the image accordingly:
\[ \text{area is } 18.9 \, \text{km}^2 \] (don't round)
### Summary
Graphically, the triangle and the calculations demonstrate how to determine the area of a triangular shape using its base and height. Understanding this concept is fundamental in geometry and can be applied to various practical and theoretical problems.
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