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
Can you solve step by step ?
![### Find the Area and Perimeter
The image displays a geometric figure with specified dimensions. The shape consists of a larger quadrilateral attached to a smaller rectangle, creating an overall irregular shape.
#### Dimensions:
- The length of the top side is 5 feet.
- The length of the bottom side is 5 feet.
- The leftmost vertical segment is 2 feet.
- The rightmost vertical segment is 2 feet.
- The height from the top side to the bottom side, inclusive of the smaller rectangle, is segmented into 2 feet + 4 feet + 2 feet = 8 feet.
#### Detailed Diagrams:
- **Top quadrilateral:**
- Top horizontal side: 5'
- Right vertical side: 4'
- The left and right slanting segments of the quadrilateral appear to make the top part’s overall vertical length shorter than the bottom, contributing to the area calculation.
- **Bottom rectangle:**
- Left vertical side: 2'
- Bottom horizontal side: 5'
- Right vertical side: 2'
To find the area and perimeter, we must break down the shape into simpler geometric figures, calculate each area and perimeter, then sum up for the irregular shape.
1. **Area Calculation:**
- Top quadrilateral area: Let's treat it as a truncated rectangle for simplicity.
- Bottom rectangle area:
Area = Length x Width = 5' x 2' = 10 square feet.
Combining these, we would likely subtract the non-overlapping area at the bottom part:
\[
\text{Total Area} = \text{Top quadrilateral approximate area} + 10 \text{ square feet}
\]
2. **Perimeter Calculation:**
- Sum of all outer sides.
- We add each unique segment around the shape to find the perimeter:
\[
\text{Perimeter} = 5' (top) + 5' (bottom) + 4' (right vertical of top) + 2' (right vertical of rectangle) + 2' (left vertical of rectangle) + 2' (offset at bottom + side) = 20 \text{ feet}
\]
**Note:** This is a conceptual overview. The exact method of calculating the top area's contribution should be verified with accurate mathematical segmentation if considering trapezoidal formulas or subdivision into simpler shapes](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F991e73b4-6c7b-4bec-a3ba-61e369206183%2F3d36cb42-a74f-4802-a7d4-e32d636e5cb8%2Fd1g0qq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Find the Area and Perimeter
The image displays a geometric figure with specified dimensions. The shape consists of a larger quadrilateral attached to a smaller rectangle, creating an overall irregular shape.
#### Dimensions:
- The length of the top side is 5 feet.
- The length of the bottom side is 5 feet.
- The leftmost vertical segment is 2 feet.
- The rightmost vertical segment is 2 feet.
- The height from the top side to the bottom side, inclusive of the smaller rectangle, is segmented into 2 feet + 4 feet + 2 feet = 8 feet.
#### Detailed Diagrams:
- **Top quadrilateral:**
- Top horizontal side: 5'
- Right vertical side: 4'
- The left and right slanting segments of the quadrilateral appear to make the top part’s overall vertical length shorter than the bottom, contributing to the area calculation.
- **Bottom rectangle:**
- Left vertical side: 2'
- Bottom horizontal side: 5'
- Right vertical side: 2'
To find the area and perimeter, we must break down the shape into simpler geometric figures, calculate each area and perimeter, then sum up for the irregular shape.
1. **Area Calculation:**
- Top quadrilateral area: Let's treat it as a truncated rectangle for simplicity.
- Bottom rectangle area:
Area = Length x Width = 5' x 2' = 10 square feet.
Combining these, we would likely subtract the non-overlapping area at the bottom part:
\[
\text{Total Area} = \text{Top quadrilateral approximate area} + 10 \text{ square feet}
\]
2. **Perimeter Calculation:**
- Sum of all outer sides.
- We add each unique segment around the shape to find the perimeter:
\[
\text{Perimeter} = 5' (top) + 5' (bottom) + 4' (right vertical of top) + 2' (right vertical of rectangle) + 2' (left vertical of rectangle) + 2' (offset at bottom + side) = 20 \text{ feet}
\]
**Note:** This is a conceptual overview. The exact method of calculating the top area's contribution should be verified with accurate mathematical segmentation if considering trapezoidal formulas or subdivision into simpler shapes
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning