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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![### Explanation of the Image:
**Question:**
What is the total area, in square centimeters, of the shaded sections of the trapezoid below?
**Diagram:**
- The diagram shows a trapezoid with two parallel sides (bases) and two non-parallel sides.
- The top base (shorter parallel side) of the trapezoid measures 6.1 cm.
- The bottom base (longer parallel side) of the trapezoid measures 9.5 cm.
- The height of the trapezoid from the top base to the bottom base is 6.2 cm.
- The bottom section within the trapezoid shows a horizontal line segment parallel to the bases, measuring 8.1 cm.
**Steps to calculate the area of the trapezoid:**
1. Identify and label the lengths of the bases (b1 and b2) and the height (h):
- b1 (top base) = 6.1 cm
- b2 (bottom base) = 9.5 cm
- h (height) = 6.2 cm
2. Use the formula for the area of a trapezoid:
\[ \text{Area} = \frac{1}{2} \times (b1 + b2) \times h \]
3. Substitute the given measurements into the formula:
\[ \text{Area} = \frac{1}{2} \times (6.1 \, cm + 9.5 \, cm) \times 6.2 \, cm \]
\[ \text{Area} = \frac{1}{2} \times 15.6 \, cm \times 6.2 \, cm \]
\[ \text{Area} = \frac{1}{2} \times 96.72 \, cm^2 \]
\[ \text{Area} = 48.36 \, cm^2 \]
Therefore, the total area of the trapezoid is **48.36 square centimeters**.
### Clarification on the Diagram:
- The additional line segment of 8.1 cm inside the trapezoid does not affect the total area as it is simply a partition within the total shape and does not change the dimensions of the overall trapezoid calculations.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb223a19b-0fd0-443c-881a-6f762159fad5%2F8986621f-8c0c-4d1a-8bc7-c7cb56b7d78a%2F8mfhet9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Explanation of the Image:
**Question:**
What is the total area, in square centimeters, of the shaded sections of the trapezoid below?
**Diagram:**
- The diagram shows a trapezoid with two parallel sides (bases) and two non-parallel sides.
- The top base (shorter parallel side) of the trapezoid measures 6.1 cm.
- The bottom base (longer parallel side) of the trapezoid measures 9.5 cm.
- The height of the trapezoid from the top base to the bottom base is 6.2 cm.
- The bottom section within the trapezoid shows a horizontal line segment parallel to the bases, measuring 8.1 cm.
**Steps to calculate the area of the trapezoid:**
1. Identify and label the lengths of the bases (b1 and b2) and the height (h):
- b1 (top base) = 6.1 cm
- b2 (bottom base) = 9.5 cm
- h (height) = 6.2 cm
2. Use the formula for the area of a trapezoid:
\[ \text{Area} = \frac{1}{2} \times (b1 + b2) \times h \]
3. Substitute the given measurements into the formula:
\[ \text{Area} = \frac{1}{2} \times (6.1 \, cm + 9.5 \, cm) \times 6.2 \, cm \]
\[ \text{Area} = \frac{1}{2} \times 15.6 \, cm \times 6.2 \, cm \]
\[ \text{Area} = \frac{1}{2} \times 96.72 \, cm^2 \]
\[ \text{Area} = 48.36 \, cm^2 \]
Therefore, the total area of the trapezoid is **48.36 square centimeters**.
### Clarification on the Diagram:
- The additional line segment of 8.1 cm inside the trapezoid does not affect the total area as it is simply a partition within the total shape and does not change the dimensions of the overall trapezoid calculations.
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