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8. What is the area of the figure below, given that each side of the regular hexagon has length 32.4 cm, and the apothem is about 25.7 cm? Round your answer to the nearest hundredth when appropriate. Fo)(40)-A2 alarmai 16s to sois.ari Area =

8. What is the area of the figure below, given that each side of the regular hexagon has length 32.4 cm, and the apothem is about 25.7 cm? Round your answer to the nearest hundredth when appropriate. Fo)(40)-A2 alarmai 16s to sois.ari Area =

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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### Problem Statement: **8. What is the area of the figure below, given that each side of the regular hexagon has a length of 32.4 cm, and the apothem is about 25.7 cm? Round your answer to the nearest hundredth when appropriate.** (Here is an image of a regular hexagon.) **Area ≈ ______________________** ### Explanation: The problem is asking for the area of a regular hexagon, given the side length and the apothem. **Definitions and Formulas:** - **Regular Hexagon:** A polygon with six equal sides and angles. - **Side Length (s):** 32.4 cm - **Apothem (a):** 25.7 cm **Formula for the Area of a Regular Hexagon:** \[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \] Since the hexagon has six sides, its perimeter (P) can be calculated as: \[ \text{Perimeter (P)} = 6 \times \text{Side Length (s)} \] **Step-by-Step Solution:** 1. **Calculate the Perimeter:** \[ \text{Perimeter} = 6 \times 32.4 \, \text{cm} \] \[ \text{Perimeter} = 194.4 \, \text{cm} \] 2. **Apply the formula for the Area:** \[ \text{Area} = \frac{1}{2} \times 194.4 \, \text{cm} \times 25.7 \, \text{cm} \] \[ \text{Area} ≈ \frac{1}{2} \times 194.4 \times 25.7 \] \[ \text{Area} ≈ 0.5 \times 194.4 \times 25.7 \] \[ \text{Area} ≈ 2497.68 \, \text{cm}^2 \] **Answer:** The area of the hexagon is approximately 2497.68 cm².
Transcribed Image Text:### Problem Statement: **8. What is the area of the figure below, given that each side of the regular hexagon has a length of 32.4 cm, and the apothem is about 25.7 cm? Round your answer to the nearest hundredth when appropriate.** (Here is an image of a regular hexagon.) **Area ≈ ______________________** ### Explanation: The problem is asking for the area of a regular hexagon, given the side length and the apothem. **Definitions and Formulas:** - **Regular Hexagon:** A polygon with six equal sides and angles. - **Side Length (s):** 32.4 cm - **Apothem (a):** 25.7 cm **Formula for the Area of a Regular Hexagon:** \[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} \] Since the hexagon has six sides, its perimeter (P) can be calculated as: \[ \text{Perimeter (P)} = 6 \times \text{Side Length (s)} \] **Step-by-Step Solution:** 1. **Calculate the Perimeter:** \[ \text{Perimeter} = 6 \times 32.4 \, \text{cm} \] \[ \text{Perimeter} = 194.4 \, \text{cm} \] 2. **Apply the formula for the Area:** \[ \text{Area} = \frac{1}{2} \times 194.4 \, \text{cm} \times 25.7 \, \text{cm} \] \[ \text{Area} ≈ \frac{1}{2} \times 194.4 \times 25.7 \] \[ \text{Area} ≈ 0.5 \times 194.4 \times 25.7 \] \[ \text{Area} ≈ 2497.68 \, \text{cm}^2 \] **Answer:** The area of the hexagon is approximately 2497.68 cm².
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