Ore8.0 ED 50. The area formula for a regular polygon is ap. Find the area of a regular hexagon with side length of 16 cm and apothem length of 13.9 cm. A. 222.4 cm² B. 556 cm2 C. 667.2 cm² D.778.4 cm² (13-9X16) 2224 ста 812 doig
Ore8.0 ED 50. The area formula for a regular polygon is ap. Find the area of a regular hexagon with side length of 16 cm and apothem length of 13.9 cm. A. 222.4 cm² B. 556 cm2 C. 667.2 cm² D.778.4 cm² (13-9X16) 2224 ста 812 doig
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
Related questions
Question
#50
![### Geometry Quiz Solutions
#### Question 49:
**What is the volume of a prism with length 9 cm, width 5 cm, and height 4 cm?**
**Answer Options:**
A. 202 cm³
B. 180 cm³
C. 99 cm³
D. 81 cm³
**Solution:**
To find the volume of the prism, we use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Substituting the given values:
\[ \text{Volume} = 9 \, \text{cm} \times 5 \, \text{cm} \times 4 \, \text{cm} = 180 \, \text{cm}³ \]
Therefore, the correct answer is B. 180 cm³.
#### Question 50:
**The area formula for a regular polygon is \(\frac{1}{2} \times Perimeter \times Apothem\). Find the area of a regular hexagon with side length of 16 cm and apothem length of 13.9 cm.**
**Answer Options:**
A. 222.4 cm²
B. 556 cm²
C. 667.2 cm²
D. 778.4 cm²
**Solution:**
First, find the perimeter of the regular hexagon. Since it is a hexagon, it has 6 sides.
\[ \text{Perimeter} = 6 \times \text{side length} = 6 \times 16 \, \text{cm} = 96 \, \text{cm} \]
Next, use the area formula for a regular polygon:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} = \frac{1}{2} \times 96 \, \text{cm} \times 13.9 \, \text{cm} \]
Calculating,
\[ \text{Area} = \frac{1}{2} \times 96 \, \text{cm} \times 13.9 \, \text{cm} = 48 \, \text{cm} \times 13.9 \,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9d544791-a77c-4b5e-888b-2e8a4014205c%2Faeff1447-82e6-4d06-944d-10aa106332bb%2Funmfa0a_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Geometry Quiz Solutions
#### Question 49:
**What is the volume of a prism with length 9 cm, width 5 cm, and height 4 cm?**
**Answer Options:**
A. 202 cm³
B. 180 cm³
C. 99 cm³
D. 81 cm³
**Solution:**
To find the volume of the prism, we use the formula for the volume of a rectangular prism:
\[ \text{Volume} = \text{length} \times \text{width} \times \text{height} \]
Substituting the given values:
\[ \text{Volume} = 9 \, \text{cm} \times 5 \, \text{cm} \times 4 \, \text{cm} = 180 \, \text{cm}³ \]
Therefore, the correct answer is B. 180 cm³.
#### Question 50:
**The area formula for a regular polygon is \(\frac{1}{2} \times Perimeter \times Apothem\). Find the area of a regular hexagon with side length of 16 cm and apothem length of 13.9 cm.**
**Answer Options:**
A. 222.4 cm²
B. 556 cm²
C. 667.2 cm²
D. 778.4 cm²
**Solution:**
First, find the perimeter of the regular hexagon. Since it is a hexagon, it has 6 sides.
\[ \text{Perimeter} = 6 \times \text{side length} = 6 \times 16 \, \text{cm} = 96 \, \text{cm} \]
Next, use the area formula for a regular polygon:
\[ \text{Area} = \frac{1}{2} \times \text{Perimeter} \times \text{Apothem} = \frac{1}{2} \times 96 \, \text{cm} \times 13.9 \, \text{cm} \]
Calculating,
\[ \text{Area} = \frac{1}{2} \times 96 \, \text{cm} \times 13.9 \, \text{cm} = 48 \, \text{cm} \times 13.9 \,
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