Question

50 POINTS NEED HELP ASAP

Round to nearest hundredth 0.00
Apothem of the polygon=__m
Perimeter=__M

Use the perimeter and apothem you
calculated
Area of the polygon=__m²

Answer 1

Answer :

• apothem = 24.25 m
• perimeter = 168 m
• area = 2,036.89 m^2

Explanation :

apothem of a regular hex is given by,

• apothem = (√3/2)*s

plug in,

• apothem = (√3/2)*28 m
• apothem = 14 √3 m
• apothem = 24.25 m ( to the nearest hundredth )

perimeter is the sum of all the sides of a polygon

• perimeter = 6*28 m
• perimeter = 168 m

thus,

the area of the hex would be

• 1/2*apothem*perimeter

1/2*14√3m*168m

• 1176√3 m^2
• 2036.89 m^2 .

Answer 2

Answer:

$\sf Apothem(a) = 24.25 \, \textsf{m}$

$\sf Perimeter (P)168 \, \textsf{m}$

$\sf Area(A) = 2036.89 \, \textsf{m}^2$

Step-by-step explanation:

To calculate the apothem, perimeter, and area of a regular polygon with side length $\sf 28 \, \textsf{m}$ and $\sf 6$ sides, we can use the following formulas:

Apothem ($\sf a$) of a regular polygon:

$\large\boxed{\boxed{\sf a = \dfrac{s}{2 \times \tan\left(\dfrac{\pi}{n}\right)}}}$

Where:

• $\sf s$ is the length of one side
• $\sf n$ is the number of sides

Perimeter ($\sf P$) of a regular polygon:

$\large\boxed{\boxed{\sf P = n \times s}}$

Where:

• $\sf n$ is the number of sides
• $\sf s$ is the length of one side

Area ($\sf A$) of a regular polygon:

$\large\boxed{\boxed{\sf A = \dfrac{1}{2} \times a \times P }}$

Where:

• $\sf a$ is the apothem
• $\sf P$ is the perimeter

Given:

• Side length ($\sf s$) = $\sf 28 \, \textsf{m}$
• Number of sides ($\sf n$) = $\sf 6$

Let's calculate:

Apothem ($\sf a$):

$\sf a = \dfrac{28}{2 \times \tan(\dfrac{\pi}{6})}$

$\sf a = \dfrac{28}{2 \times \tan(30^\circ)}$

$\sf a = \dfrac{28}{2 \times 0.5773502691896}$

$\sf a = \dfrac{28 }{2 \times \sqrt{3}}$

$\sf a = \dfrac{28}{1.1547005383792}$

$\sf a \approx 24.248711305964$

$\sf a \approx 24.25 \, \textsf{m (in nearest hundredth)}$

Perimeter ($\sf P$):

$\sf P = 6 \times 28$

$\sf P = 168 \, \textsf{m}$

Area ($\sf A$):

$\sf A = \dfrac{1}{2} \times 24.248711305964 \times 168$

$\sf A = \dfrac{1}{2} \times 48.497 \times 168$

$\sf A = 2036.8917497009$

$\sf A \approx 2036.89 \, \textsf{m ^2 (in nearest hundredth)}$

In summary:

$\sf Apothem(a) = 24.25 \, \textsf{m}$

$\sf Perimeter (P)168 \, \textsf{m}$

$\sf Area(A) = 2036.89 \, \textsf{m}^2$