NO LINKS!! URGENT HELP PLEASE!!
O is the center of the regular dodecagon below. Find its area. Round to the nearest tenth.

Answer:

80.4 square units.

Step-by-step explanation:

solution Given:

apothem(a)=5

no of side(n)= 12

Area(A)-?

The area of a regular polygon can be found using the following formula:

[tex]\boxed{\bold{Area =\frac{1}{2}* n * s * a}}[/tex]

where:

In this case, we have:

First, we need to find S.

We can find the length of one side using the following formula:

[tex]\boxed{\bold{s = 2 * a * tan(\frac{\pi}{n})}}[/tex]

substituting value:

[tex]\bold{s = 2 * 5 * tan(\frac{\pi}{12})=2.679}[/tex]   here π is 180°

To find the area substituting value in the above area's formula:

[tex]\bold{Area = \frac{1}{2}* 12 * 2.679 * 5=80.37\: sqaure\: units}[/tex]

in nearest tenth 80.4 square units.

Therefore, the area of the regular polygon is 80.4 square units.

Answer:

80.4 square units (nearest tenth)

Step-by-step explanation:

The given diagram shows a regular dodecagon (12-sided polygon) with an apothem of 5 units.

The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of one of its sides.

We can calculate the side length of a regular polygon given its apothem using the following formula:

[tex]\boxed{\begin{minipage}{5.5cm}\underline{Apothem of a regular polygon}\\\\$a=\dfrac{s}{2 \tan\left(\dfrac{180^{\circ}}{n}\right)}$\\\\where:\\\phantom{ww}$\bullet$ $s$ is the side length.\\ \phantom{ww}$\bullet$ $n$ is the number of sides.\\\end{minipage}}[/tex]

Substitute n = 12 and a = 5 into the equation to create an expression for s:

[tex]5=\dfrac{s}{2 \tan \left(\dfrac{180^{\circ}}{12}\right)}[/tex]

[tex]s=10\tan \left(15^{\circ}\right)[/tex]

Now we can use the standard formula for an area of a regular polygon:

[tex]\boxed{\begin{minipage}{6cm}\underline{Area of a regular polygon}\\\\$A=\dfrac{n\cdot s\cdot a}{2}$\\\\where:\\\phantom{ww}$\bullet$ $n$ is the number of sides.\\ \phantom{ww}$\bullet$ $s$ is the length of one side.\\ \phantom{ww}$\bullet$ $a$ is the apothem.\\\end{minipage}}[/tex]

Substitute the found expression for s, n = 12 and a = 5 into the formula and solve for A:

[tex]A=\dfrac{12 \cdot 10\tan \left(15^{\circ}\right) \cdot 5}{2}[/tex]

[tex]A=\dfrac{600\tan \left(15^{\circ}\right)}{2}[/tex]

[tex]A=300\tan \left(15^{\circ}\right)[/tex]

[tex]A=80.3847577...[/tex]

[tex]A=80.4\; \sf square\;units\;(nearest\;tenth)[/tex]

Therefore, the area of a regular dodecagon with an apothem of 5 units is 80.4 square units, rounded to the nearest tenth.

Check your solution!

5 • x = 12

#5 Mr. Awesome & Mrs. Amazing had their students count how many pencils they each had in their pencil boxes. The box plots display the data for both classes. NUMBER OF PENCILS Mc. Awesome's Class Mrs Amazing's Class 앵 0 1 2 3 10 12 13 14 4 15 16 17 18 19 20 Which statement is best supported by the information in the box plots? A) The data for Mr. Awesome's class is more symmetrical than the data for Mrs. Amazing's class. B) The interquartile range of the data for Mr. Awesome's class is less than the interquartile range of the data for Mrs. Amazing's class. The median number of the data for Mr. Awesome's class is less than the median number of the data for Mrs. Awesome's class. D) The range of the data for Mc Awesome's class is less than the range of the data for Mrs. Amazing's class. Amazno Mihemetics​

Which graph best represents the equation x + 5y = 25?
A.
B.
C.
D.

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in one week. Fourteen people answered that they generally sell five cars; nineteen generally sell six cars; twelve generally sell seven cars; nine generally sell eight cars; eleven generally sell nine cars. Calculate the following. (Round your answer to two decimal places.)Data Value (# cars) Frequency Relative Frequency Cumulative Relative Frequency

242m/min express this in km/h​

HELPPPPPP MEEEE PLEASE AND THANK YOU ILL MARK YOU BRAINLIEST

HELP!!! An electronics company designed a cardboard box for its new line of air purifiers. The figure shows the dimensions of the box.



The amount of cardboard required to make one box is ___
square inches.

5 more than the product of a number and 4 is equal to 3 use variable y for unknown number

5 less than twice the length equals 11 as an algebraic equation

Jerry has a jar with 273 marbles in it. The jar can hold 1,000 marbles in all
which equation can be used to find m, the number of marbles still needed to fill
the jar
273
1,000
1,000
1,000 1 273 m
1.000
Done >

Lunch costs $2.25 per day. An equation showing the relationship between
the number of days, d, and the total cost of lunch, c, is c = 2.25d What is
the dependent variable?*

d = the number of days
c = the total cost of lunch

What is the answer?

please help Use the expression 8a + 16c.
Part A
Factor the expression using the GCF.
A. 2(4a + 8c)
B. 4(2a + 4c)
C. 8(a + 2c)
D. 16(12a + c)
Part B
What is the value of the expression when a = –5 and c = –1? Enter your answer in the box.

Solve this systems of equations.
Will mark brainlest!

{4y + 7x =6}

{4y + 7x = -5}

What is the equation for the volume of a Cylinder? And a can of baked beans is 11cm by 3.5cm, a can of soda pop is 13cm by 4cm. What is the difference between the volume of the baked beans and the volume of the soda pop? Please explain using math vocabulary, and how you solved this problem.

Geometry question plz someone help me

Find the missing lengths or missing angles

A Mater Exam
Q2 SA 1
4 Points
What is the slope of a line that is perpendicular to the line f(x) = 2x + 6? Justify your answer
by typing out your calculations or explaining your reasoning.
Enter your answer here
Please select file(s)
Select file(s)

Danny charges $27 for 3 hours of swimming lessons, Martin charges $30 for 2 hours of swimming lessons. Who offers a better deal?

-2, -4, -8,-16, ... Find the explicit formula

equation.
1. h - 9= 2h - 1

Anyone can help me with this

I need help with geometry shapes

The price of stock in a software company drops by $42.60 over a 16-day period. On average, how much does it drop per day?
$2.66
$0.37
$26.60

$2.60

Which numbers make a true statement when placed in the box?
11.436 > 0
Select each correct answer.
11.422
11.484
11.621
11.286
o
Please help

Interest of 1 million dollars 23% and 6 years please solve and will give brainliest to correct answer

Is parallelogram VWXY a rhombus?

Which expression is equivalent to 4r2/514.3V5r8, if x=0?
A. 12 r105
B. 6018
C. 35r18
D.
710/5
Look at picture please

Find the area (in square inches) of the parallelogram.

DI
A rectangle measures x cm
by (x + 4)cm.What are the width and length of the rectangle?​

In the somewhat less than towering ski slopes of northeastern Iowa new skiers come to learn to ski. On Big Bunny Slope skiers will fail to make the turn at Big Bend. On Little Bunny Slope, skiers will sometimes tumble at Little Hill. The ski instructors send the new skiers down the two slopes in groups of 30, wait a few moments, and then send the Ski Patrol Ambulance down after them, stopping at Big Bend and then Little Hill. The skiers descend the slopes far enough apart that they don't run into each other, so their spills are all independent.

Required:
a. The probability that a random new skier in the group will need to be carried to the First Aid Station after a spill at Big Bend is 0.35. If we define the random variable B = number of new skiers needing to be driven to the First Aid Station from Big
Bend, we can model this situation as a binomial chance experiment. What is the mean and standard deviation of B?
b. The probability that a random new skier in the group will need to be carried to the First Aid Station after a spill at Little Hill is 0.15. If we define the random variable L = number of new skiers needing to be driven to the First Aid Station from Little Hill, what is the mean and standard deviation of L?