Solve the perimeter. **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.

Given, Diameter of semicircle, D = 40 ft radius, r = D2 = 40 ft2 = 20 ft Circumference of the…

Answered: Find the perimeter of the composite…

Math

Geometry

Find the perimeter of the composite figure. Show your work. 21 ft - 15 ft 40 ft

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.

**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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