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

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

Elementary Geometry For College Students, 7e
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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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.
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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