A hexagon with an apothem of 14.7 inches is shown. a regular hexagon has an apothem of 14.7 inches and a perimeter of 101.8 inches. what is the area of the hexagon? square inches

Answers

Answer 1

The area of the considered regular hexagon which has got 14.7 inches of apothem and a perimeter of 101.8 inches is 748.2 sq. inches.

What is apothem?

Apothem for a regular polygon is a line segment which originates from the center of the regular polygon and touches the mid of one of the sides of the regular polygon. It is perpendicular to the regular polygon's side it touches.

Regular polygons have all side same and that apothem bisects the side in two parts, (provable by symmetry).

Consider the diagram attached below.

The area of the regular hexagon considered = 6 times (area of triangle ABC) (because of symmetry).

Also, we have:

Area of triangle ABC = 2 times (Area of triangle ABD).

Thus, we get:
Area of the considered hexagon = 6×2×(Area of triangle ABD)

Area of the considered hexagon = 12×(Area of triangle ABD)

Perimeter of a closed figure = sum of its sides' lengths.

There are 6 equal sides in a regular hexagon (due to it being regular).

Thus, if each side is of 'a' inch length, then:

Perimeter = 6×a inches

[tex]101.8 = 6a\\\\\text{Dividing both the sides by 6, to get 'a' on one side}\\\\a = \dfrac{101.8}{6} \approx 16.967 \: \rm inches[/tex]

This is bisected by the apothem.

Thus, we get:
Length of the line segment BD = |BD| = a/2 ≈ 8.483 inches

Since it is given that the length of the apothem = |AD| = 14.7 inches, therefore, we get:

[tex]\text{Area of ABD} = \dfrac{1}{2} \times \rm base \times height \approx \dfrac{14.7 \times 8.483}{2} \approx 62.35 \: \rm in^2[/tex]

Thus, we get:

Area of the considered hexagon = 12×(Area of triangle ABD)

Area of the considered hexagon [tex]\approx 12 \times 62.35 = 748.2 \: \rm in^2[/tex]

Thus, the area of the considered regular hexagon which has got 14.7 inches of apothem and a perimeter of 101.8 inches is 748.2 sq. inches.

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A Hexagon With An Apothem Of 14.7 Inches Is Shown. A Regular Hexagon Has An Apothem Of 14.7 Inches And
Answer 2

Answer:

748.23

Step-by-step explanation:

On edge


Related Questions

Find the value of x. Assume that lines which appear to be tangent to the circle are tangent. A) 1 B) 3 C) 4 D) 6

Answers

Answer: D

Step-by-step explanation:

find the volume of the prism

Answers

Answer:336 cubic inches

Step-by-step explanation:
Formula: L•w•h
14•4•6=336

Given that 2x + 1 : x + 2 = x+8 : 3x-4
Find the possible values of x.

Answers

Answer:

First we have to same the bases.

As we know 8=2^3.

Replace 8 with 2^3.

Like this .

2^3x=2^3(2x+1).

Now 3x=3(2x+1) distribute 3 by the Barker.

3x=6x+3.

6x+3=3x.

6x-3x=-3.

3x=-3.

X=-1.

Step-by-step explanation:

It is Given that 2x + 1 : x + 2 = x+8 : 3x-4 therefore, the possible value of x is -1.

How to find the system of equations needed to solve an equation?

An equation usually consists of equality of two mathematical expressions. Let it be

A = B

. If we take them to be equal to third variable, then:

A = B = C

type of equation is obtained.

We can then take it as a system of two equations as:

A = C\\ B=C

The solution to this system will give us the solution to the considered equation.

The solution to an equation is finding values of the variable included in the considered equation for which the equation considered evaluates to be true.

Given that 2x + 1 : x + 2 = x+8 : 3x-4

First we have to same the bases.

As we know [tex]8=2^3.[/tex]

[tex]2^{3x}=2^{3(2x+1)}.[/tex]

Now 3x=3(2x+1) distribute 3 by the Barker.

[tex]3x=6x+3.\\6x+3=3x.\\6x-3x=-3.\\3x=-3.\\x=-1.[/tex]

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please help its late and I need to finish this. there are more if you can solve this

Answers

Answer:

Plow - is used for tilling largefurrows and inter row cultivation. WhTractor - Used to pull disc plow and disc harrow in preparing much bigger area of land Down is used for cleaning the ground and leveling the topsoil Barrow - is used for hauling trash, manures, fertilizers, plant

The sum of 2 numbers is 8 and their difference is 2
what are the 2 numbers?

Answers

Answer:

a=5

b=3

Step-by-step explanation:

a+b=8

a-b=2

2a=10

a=5

b=3

Answer:

5 and 3

Step-by-step explanation:

Sum is addition

Difference is subtraction

5 + 3 = 8 which means the sum of these 2 numbers is 8

5 - 3 = 2 which means the difference of these 2 numbers is 2

6.
Viola drives 170 m up a hill that makes an angle of 6° with the horizontal. Rounded to the nearest tenth of a meter, what horizontal distance has she covered?

169.1 m

17.8 m

1,617.4 m

171.5 m

Answers

Answer:

  (a)  169.1 m

Step-by-step explanation:

The diagram shows you the distance (x) will be shorter than 170 m, but almost that length. The only reasonable answer choice is ...

  169.1 m

__

The relevant trig relation is ...

  Cos = Adjacent/Hypotenuse

The leg of the right triangle adjacent to the marked angle is x, and the hypotenuse is 170 m. Putting these values into the equation, you have ...

  cos(6°) = x/(170 m)

  x = (170 m)cos(6°) ≈ (170 m)(0.994522) ≈ 169.069 m

The horizontal distance covered is about 169.1 meters.

_____

Additional comment

Expressed as a percentage, the slope of this hill is tan(6°) ≈ 10.5%. It would be considered to be a pretty steep hill for driving.

Regular price $174 discount
40% find the sale price round to the nearest cent if necessary

Answers

Answer:

69.6 70 to the nearest cent

Step-by-step explanation:

I don't know how to explain

A 9-foot roll of wrapping paper costs $6.03. What is the price per yard?

Answers

~Denki Kaminari here~

so what we're going to do is, find the cost of wrapping paper per foot,

6.03 divided by 9 = 0.67

now we're going to convert the 9ft into yards,

1 yard= 3ft so, there are 3 yards.

now that we know that there are 3 ft in one yard, we are going to multiply 0.67 by 3

0.67x3= 2.01

so, we got $2.01 per yard

hope this helps :D

Solve the inequality. | 7x + 5 | > 0

Answers

Answer:

x

=−

7

5

Step-by-step explanation:

Can someone please help me!


#BRAINLIEST​

Answers

1- Ferald follows school rules
2- Lex and Jaye are gems
3- Jay loves adbobo and beef stew
4- Jake's best friend is his dog
5- Kim has self-discipline

What is the surface area of the cube below?

Answers

Answer:

I dont see a cube but...

Step-by-step explanation:

A cube has 6 faces. The area of each face is found by squaring the length of the side. Multiply the area of one face by the number of faces to get the total surface area of the cube.

A=6a2

Assuming that the availability of cherries and the availability of asparagus are independent of each other, which market should Elena choose to maximize her chance of buying both?

Answers

Answer:

north market, .44

Step-by-step explanation:

I need help with this and how to solve it

Answers

60 plus 75 equals 135. 180 (sum of angles in a triangle) minus 135 is 45 degrees which matches size in picture.
Other angle 180-45 which is 135.

Which graph represents the solution to the system of inequalities?


StartLayout Enlarged left-brace first row x squared + 4 y squared less-than 64 second row y greater-than 3 Superscript x EndLayout


Answer is D

Edge 2022

Answers

The answer is D :) YW!

Balance the nuclear reaction equation for the beta minus decay of iodine-131 by completing the missing numbers. superscript 131 subscript 53 upper i right arrow superscript question mark subscript 54 upper x e plus superscript 0 subscript question mark e. the superscript of xenon is . the subscript of the electron is .

Answers

Beta minus decay has to do with the loss of an electron.  The superscript on the daughter nucleus is 131 while the subscript  is 54;

What is a beta minus decay?

The term beta minus decay has to do with the loss of an electron. The daughter nucleus so formed is always going to have an atomic number that is greater than that of the parent by 1 unit.

The complete nuclear reaction here is; [tex]\frac{131}{53} I ------- > \frac{131}{54} Xe + \frac{0}{-1} e[/tex] . The  daughter nucleus here is Xe while the parent nucleus is I.

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Answer:

The superscript of xenon is 131

The subscript of the electron is -1

Step-by-step explanation:

What is the perimeter of parallelogram ABCD?

Answers

Answer:

18 cm

Step-by-step explanation:

4+5+4+5=18

or

2(a+b)

2(4+5)

2(9)

18

Which number has an absolute value
greater than |-3|? Select all that apply.
b.|-5|
c. |9|
d. |1|
e. |7|
f. l-1|

Answers

Answer:

The number with an absolute value (distance away from zero on a number line) that is greater than 5 will be: A. -6.

Absolute value of any number is simply the distance of that number from point zero (0) on a number line.

Thus,

-6 is 6 units from 0.

6 is also 6 units away from 0.

-5 is 5 units from 0.

5 is also 5 units from 0.

The absolute value of -5 is 5.

The absolute value of -6 is 6.

Therefore, the number with an absolute value (distance away from zero on a number line) that is greater than 5 will be: A. -6.

Learn more here:

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Step-by-step explanation:

The ratio of the number of pineapples for a chocolate fondue dessert to people served is 1 to 5. If Deb wants to serve 80 people, how many pineapples will Deb use?

Answers

Answer:

16:80

Step-by-step explanation:

80 people * ( 1 pineapple / 5 people) = 16

Sam confirmed there will be 192 guests at his party. He thinks each guest will eat
about .25 lb of hamburger, so he decides to order .25 x 200 = 50 lb
What did he use to determine the amount to order?

Answers

Answer:

Sam used estimation. He rounded the amount of guests (192) to the nearest hundred (200).

Find the measure of arc FD

Answers

Answer: 49 degrees

Step-by-step explanation:

Amana walks along oak from point a to b. to the nearest foot, how far does she walk? 75 ft 226 ft 307 ft 347 ft

Answers

Answer:

266

Step-by-step explanation:

Answer:226

Step-by-step explanation:

Find the total surface area of this triangular prism.
25 cm
24 cm
10 cm
14 cm

Answers

Answer:

Step-by-step explanation:

[tex]\boxed{\text{Area of triangular prism = length*(a+b+c) + 2*base area}}[/tex]

Here a, b,c are the sides of the triangle.

a = 14 cm ; b = c = 25 cm  and length = 10 cm

[tex]\boxed{\text{Base area=2*$\dfrac{1}{2}*base*height$=base *height}}[/tex]

base = a = 14 cm & h = 24 cm

Base area = 14*24

               = 336 cm²

Total surface area = 10*(14+25+25) + 336

                              = 10*64 + 336

                             = 640 + 336

                             = 976 cm²

plss help me quickly tyyy
either question 5 or six cus I need the explanation:)))​

Answers

Find FM using Pythagoras Theorem:

We're not after c^2 using pythag - rearrange it:

It don't matter were the B or A is in the equation - it'll give u the missing length you're after.

c^2 - b^2 = a^2

8^2 - 5^2 = a^2

Square root both sides to get A on its own

A= root 8^2 - 5^2

= root 39

= 6.24499....

Or

6.24cm, but FM is root 39 I'll use throughout, even if I use 6.24 in calculations, it's to make things clearer for you.

Create diagonal line from B to E - drawing right-angle triangle A to B to E back to A.

AB is 16cm

AE is 8cm - given above

(because the triangle at the front & back are the same.)

Use Pythagoras Theorem for length BE:

a^2 + b^2 = c^2

16^2 + 8^2 = c^2

Square root

C = root 16^2 + 8^2

= 8 root 5

= 17.8885...

8 Square root 5 - I'll use for BE

Creat another triangle to find the angel -

B to E to (M between the length AD)

However, diagonal line B to M needed.

So, m is the mid-point of the base triangle, pretend to slice it in half from point M - this creates a mini rectangle. (ABM to MA - with M on side AD)

Now use this to find B to M:

(if MC is 5cm, BM is 5cm - on length BC)

C = root 16^2 + 5^2

= root 281

= 16.76305...

= 16.76

Create right-angle triangle:

Be to M back to B

BE= 8 root 5

EM = root 39

MB = root 281

So, the angle will be from EB to M.

EB is the hypotenuse

BM is the adjacent

AH means Cah, but the inverse

Cos-1(a/h)

Cos-1(root 281 / 8 root5) = 20.4326...

Thus, angle we're after is 20.43 degrees to 2.dp

(The easiest way for me to explain - it took a while)

Hope this helps!

if emily eats 18 cookies, which represents 30% of the bag, how many cookies are in the bag

Answers

Answer:60

Step-by-step explanation:

18 x 100= 1800. 1800/30= 60. 60 x %30= 18

The number of cookies in the bag is A = 60

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

Now , 30 % of the cookies in the bag = 18 cookies

On simplifying the equation , we get

( 30 / 100 )A = 18

Multiply by 100 on both sides , we get

30A = 1800

Divide by 30 on both sides , we get

A = 1800/30

A = 60 cookies

Hence , the number of cookies is 60

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Will give brainliest!! Can someone explain how to do this please? (Grade 10 math)

Answers

Answer:

The slop is +9, so add 9 each time

Step-by-step explanation:

Name a diameter.
8
G
E
A
FG
С
CE
B.
AB
D
BO

Answers

Answer:

FG

Step-by-step explanation:

Hello!

A diameter is a line segment that goes through the center of a circle and touches two points on the perimeter of the circle.

Here, we see two lines that touch two points of the circle (AB and FG) but only one segment, FG, goes through the center, given by the point O.

Hence, it is Option A: FG

Two major cities each have a population of
25,000 people. The population of City A
increases by about 150 people per year. The
population of City B increases by about 0.5%
per year.
Insert table from SPREADSHEET here, showing the first 5 years of population growth for both
cities.
Will City B ever have a larger population than City A? If so, what year will this occur?
Answer:
...insert the DESMOS graph that supports your answer here...

Answers

Realistically would be 20.

What is the solution to the system of equations below?

y = one-half x + 6 and y = negative three-fourths x minus 4
(–8, 2)
(–8, –1)
(8, 10)
(8, –10)

Answers

Answer:

(-8, 2)

Step-by-step explanation:

1. Set up the equations.

y = 1/2x + 6

y = -3/4x - 4

2. Set the equations to equal each other.

1/2x + 6 = -3/4x - 4

3. Move the variables to one side and the numbers to the opposite side.

6 + 4 = -3/4x - 1/2x

10 = -3/4x - 2/4x

10 = -5/4x

4. Divide 10 by -5/4.

10/ -5/4 = 10 * -4/5 (when dividing fractions, flip the fraction over)

10 * -4/5 = -40/5 = -8

x = -8

5. Plug in the x-value into one of the equations.

y = 1/2x + 6

y = 1/2(-8) + 6

y = -4 + 6

y = 2

OR

y = -3/4x - 4

y = -3/4(-8) - 4

y = 6 - 4

y = 2

Ben bowled 160 and 191 in his first two games. What must he bowl in his third game to have an average of at least 190?​

Answers

I don’t understand the question

What do we multiply 24 by to get a 100

Answers

Answer:

you cant do that, you can only get to 96 by multiplying 24 by 4, ill keep trying tho if you really need this

Step-by-step explanation:

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