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
Solve the perimeter.

Transcribed Image Text:**Title: Calculating the Perimeter of a Composite Figure**
**Objective:** Find the perimeter of the given composite figure.
**Description of the Figure:**
The figure consists of two parts:
1. **Trapezoid:**
- The top side measures 21 ft.
- The bottom side measures 40 ft.
- The slanted sides are marked with notches and measure 15 ft each.
2. **Semicircle:**
- The semicircle is attached to the bottom side of the trapezoid, which is 40 ft long (this serves as the diameter of the semicircle).
**Steps to Calculate the Perimeter:**
1. **Find the Perimeter of the Trapezoid:**
- Add the lengths of all the sides of the trapezoid.
- Trapezoid perimeter = 21 ft (top) + 15 ft (left slanted side) + 15 ft (right slanted side) + 40 ft (bottom).
2. **Calculate the Circumference of the Semicircle:**
- The formula for the circumference of a circle is \( C = \pi \times d \), where \( d \) is the diameter.
- Since the semicircle is half of a circle, its circumference is \( \frac{\pi \times 40}{2} = 20\pi \) ft.
3. **Add the Perimeters Together:**
- Perimeter of the trapezoid + circumference of the semicircle.
- Total perimeter = (21 + 15 + 15 + 40) + 20π ft.
**Conclusion:**
The final step involves adding all calculated lengths together to find the total perimeter of the composite figure. Use \(\pi \approx 3.14\) to find a numerical approximation if necessary.
**Note:** Ensure all measurements are added correctly to obtain the precise perimeter of the composite shape.
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