Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Task 5: Perimeter Formula Calculation**
**Objective:** Write a formula for the perimeter of the figure from problem #4 in terms of \( a, b, c, \) and \( d \).
**Diagram Description:**
The figure is composed of a rectangle with a semicircle on top. The rectangle has the following measurements:
- Height: \( a \)
- Base: \( b \)
The semicircle sits on top of the rectangle, sharing its width.
- The radius of the semicircle (half of the base of the rectangle): \( \frac{b}{2} \)
A diagonal line extends from the top corner of the rectangle to the edge of the semicircle, labeled \( d \).
**To find the perimeter:**
1. **Rectangle:**
- One side of length \( a \)
- One base of length \( b \)
2. **Semicircle:**
- Perimeter: \( \pi \times \frac{b}{2} \) (half of the circle's circumference)
3. **Diagonal Line:** Length \( d \)
Thus, the perimeter \( P \) can be formulated as:
\[ P = b + 2a + \pi \times \frac{b}{2} - b + d \]
\[ P = 2a + \left(\frac{\pi b}{2}\right) + d \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92ab3c20-a3cd-4c1e-8775-52ac5ed4d4cf%2F8b92c124-c17d-437d-975c-a6f7b6eedba0%2F0tjrjza_processed.png&w=3840&q=75)
Transcribed Image Text:**Task 5: Perimeter Formula Calculation**
**Objective:** Write a formula for the perimeter of the figure from problem #4 in terms of \( a, b, c, \) and \( d \).
**Diagram Description:**
The figure is composed of a rectangle with a semicircle on top. The rectangle has the following measurements:
- Height: \( a \)
- Base: \( b \)
The semicircle sits on top of the rectangle, sharing its width.
- The radius of the semicircle (half of the base of the rectangle): \( \frac{b}{2} \)
A diagonal line extends from the top corner of the rectangle to the edge of the semicircle, labeled \( d \).
**To find the perimeter:**
1. **Rectangle:**
- One side of length \( a \)
- One base of length \( b \)
2. **Semicircle:**
- Perimeter: \( \pi \times \frac{b}{2} \) (half of the circle's circumference)
3. **Diagonal Line:** Length \( d \)
Thus, the perimeter \( P \) can be formulated as:
\[ P = b + 2a + \pi \times \frac{b}{2} - b + d \]
\[ P = 2a + \left(\frac{\pi b}{2}\right) + d \]
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