Determine the total surface area of each pyramid with a regular polygon base​

Determine The Total Surface Area Of Each Pyramid With A Regular Polygon Base

Answers

Answer 1

The total surface area of the pyramid (a) is  624.32 cm² , and of pyramid (b) is 265.6 m²  .

The Total Surface Area of the Pyramid with pentagon base can be calculated using the formula

TSA = 5/2*b(a+s) ,

where b is the base length (side of pentagon)

s is the slant height ,

a is the apothem

and the Total Surface Area of the Pyramid with square base can be calculated using the formula .

TSA = b² + 2bs

where , b is the base and

s is the slant height .

Pyramid (a)

we can see from the figure that ,the pyramid has a pentagon base ,

So, the TSA will be 5/2*b(a+s) ,

in the figure , given that height =12 cm , apothem = 7.8cm

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 7.8²

(slant height) = √(12² + 7.8²)

(slant height) = √(144+60.84)

(slant height) = 14.3 cm

Substituting in TSA formula , TSA = 5/2*b(a+s)

we get ,

TSA = 5/2*11.3(7.8+14.3)

= 2.5*11.3(22.1)

= 28.25*22.1

=624.32 cm²

Pyramid (b)

we can see from the figure that ,the pyramid has a square base ,

So, the TSA will be b² + 2bs,

in the figure , given that height =12 m , apothem = 4 m

we find the slant height by Pythagoras theorem

(slant height)²=(height)²+(apothem)²

(slant height)² = 12² + 4²

(slant height) = √(12² + 4²)

(slant height) = √(144+16)

(slant height) = 12.6 m

Substituting in TSA formula , TSA = b² + 2bs

we get ,

TSA = 8² + 2*8*12.6

= 64 + 16*12.6

= 64 + 201.6

= 265.6 m²

Therefore , the total surface area of the pyramid (a) is 624.32 cm²  , and of pyramid (b) is 265.6 m² .

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Related Questions

Simplify 2/5(14–27)+2^5÷16.

Answers

We can simplify the numerical expression to get:

(2/5)*(14 - 27) + (2⁵/16) = -16/5

How to simplify the numerical expression?

Here we have the expression:

(2/5)*(14 - 27) + (2⁵/16)

Let's simplify the term in the right first, we know that:

2⁵ = 2*2*2*2*2 = 4*4*2 = 16*2 = 32

Replacing that we get:

(2⁵/16) = 32/16 = 2

Then we get:

(2/5)*(14 - 27) + (2⁵/16) = (2/5)*(14 - 27) + 2

Now we can simplify the term in the left:

(2/5)*(14 - 27) = (2/5)*(-13) = -26/5

Replacing that we get:

(2/5)*(14 - 27) + 2 = -26/5 + 2 = -26/5 + 10/5 = -16/5

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Zak has 11 shirts and 8 ties in his wardrobe. a) On Thursday morning, he picks a shirt and a tie at random from the wardrobe. How many possible combinations are there? b) On Thursday evening, he puts the tie back in the wardrobe but not the shirt. On Friday morning, he picks a shirt and a tie at random from the wardrobe again. How many possible combinations are there now?​

Answers

Answer:

c

Step-by-step explanation:

because you do 12 times 9 minus 100 wich is 125 so yeah

Someone please help me with this!!! (Will mark Brainliest)

Answers

Answer: 5/3

Step-by-step explanation:

The scale factor is the same as the ratio of the length of a side of the image to the length of the corresponding side in the preimage.

We know that N'Q'=10 and NQ=6, so the scale factor is 10/6 = 5/3.

Explain why the statement line LR ≅ line RL and ∠CBA ≅ ∠ABC are both true by the Reflexive Property of Congruence.

Answers

The reflective Property of Congruence states that any figure is congruent with itself, therefore line LR ≅ line RL and ∠CBA ≅ ∠ABC.

What is congruence?

If it is possible to superimpose one geometric figure on the other so that their entire surface coincides, that geometric figure is said to be congruent or to be in the relation of congruence.

Reflexive Property of Congruence said that an angle line segment or any shape is congruent with itself.

For example, a line segment with a length of 5 meters will be the same as another line with 5 meters or a copy of that line so both will be congruent.

Line LR and RL are the same in length thus line LR ≅ line RL.

Angle CBA and angle ABC are the same thus ∠CBA ≅ ∠ABC.

Hence "The reflective Property of Congruence states that any figure is congruent with itself, therefore line LR ≅ line RL and ∠CBA ≅ ∠ABC".

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A transversal interersects two parallel lines. The measures of a pair of alternate interior angles are 5v and 2w. The measures of a pair of same-side exterior angles (consecutive exterior) are 10w and 5v. What are the values of w and v?

Answers

Answer: [tex]v=6, w=15[/tex]

Step-by-step explanation:

The pair of alternate interior angles are congruent, so [tex]5v=2w \implies 10w=25v[/tex].

The consecutive exterior angles are supplementary, so

[tex]10w+5v=180\\\\25v+5v=180\\\\\\30v=180\\\\v=6\\\\\implies w=2.5(6)=15[/tex]

9(x+y)=3ay solve for y

Answers

When we solve the linear equation for y, we will get:

8*x/(3*a - 9) = y

That is the solution for the variable y.

How to solve the linear equation for y?

Here we have the linear equation:

9*(x + y) = 3*a*y

Where x, y, and a are variables.

We want to solve this linear equation for y, this means that we need to isolate y in one side of the equation, to do so, let's start by expanding the left side:

9*(x + y) = 3*a*y

9*x + 9*y = 3*a*y

Now we move all the terms with y to the right side.

8x = 3*a*y - 9*y = (3*a - 9)*y

Now we divide both sides by 3*a - 9 to get:

8*x/(3*a - 9) = y

That is the equation solved for y.

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Find a formula for the exponential function passing through the points (-2, 4/9) and (3,108)

Answers

Answer:

[tex]f(x)=4(3)^x[/tex]

Step-by-step explanation:

Let [tex]f(x)=ab^x[/tex].

Then,

[tex]ab^{-2}=\frac{4}{9} \\ \\ ab^3=108 \\ \\ \frac{ab^3}{ab^{-2}}=\frac{108}{4/9} \implies b^5=243 \implies b=3 \\ \\ \therefore a(3)^3=108 \\ \\ a=4 \\ \\ \therefore f(x)=4(3)^x[/tex]

F(x)= 4^3 this is because when following the delta method then plugging it into an equation this would be the answer

A dealer purchased an old car for 70,000. He spent 17,500 on its repair and painting. Due to lack of demand he had to dispose it at a loss of 12%. What was the selling price of the car?​

Answers

The selling price of the car is 77,000.

First, let's define what a selling price is.

The selling price is the price the customer pays to purchase the good.

Selling price = Cost price – (100% Loss)/100

We are told that the car cost 70,000 and that 17,500 was lost (12%) in repairs and painting.

The car's total cost is equal to 70,000 + 17,500 = 87,500.

So, the car's cost price is 87,500.

Selling price = 100/12/100 x cost price

= 100/12/100 x 87,500

= 0.88 x 87,500

= 77,000

Consequently, the car is being sold for $77,000.

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simplify 3x + 5y - x +2y

Answers

Answer:

2x + 7y

Step-by-step explanation:

first we need to align the sample sympols

like this

3x -x + 5y + 2y

then you can easily calculate

Answer:

2x+7y

Step-by-step explanation:

3x-×=2x, 5y+2y=7y

2x+7y

Rose's stamp collection is 7 less than half of Van's stamp collection, x.

Which expression represents the total number of stamps that Rose has?

Responses

7−1/2x
7 minus fraction 1 half end fraction x

7x−1/2
7 x minus fraction 1 half end fraction

1/2−7x
fraction 1 half end fraction minus 7 x

1/2x−7

Answers

Answer: 1/2x - 7

Step-by-step explanation:

1/2x represents half of Van's stamp collection and Rose has 7 less than that.

'less than' is telling you to subtract, so the answer is 1/2x - 7

Answer: 1/2x - 7

Step-by-step explanation:

1/2x represents half of Van's stamp collection and Rose has 7 less than that.

'less than' is telling you to subtract, so the answer is 1/2x - 7

yuckyew DID THIS! NOT ME!

Given the figure, find the total area of the shaded region.
-4
A
D
8.
6-
4-
2-
O
-2-
-4
2
G
S
B
The area of the shaded region is
R
6 8
-U
X
square units.

Answers

Answer:

what was one survival event you experienced

GUYS PLSSS HELPPPPPP

Answers

hi hope this helps! rmb to factorise or expand when necessary :)
U just multiple the outside number with the inside number.
5. -21 - 9p
4. 27x + 18
6. 4x - 5
7. 1m - 8
8. 12v + 42
9. Yes there equal
10. Yes there equal

Jerald is having drain issues at his home and decides to call a plumber. The plumber charges $35 to come to his house and $50 for every hour they work. If the plumber charges Jerald a total of $190, how many hours did the plumber work?
Write and solve an equation to determine the number of hours worked by the plumber.

50x + 35 = 190; x = 3.1 hours

50x − 35 = 190; x = 4.5 hours

35x + 50 = 190; x = 4 hours

35x − 50 = 190; x = 6.9 hours

Answers

50x+35=190; x=3.1 hours is the correct answer because 35 would be you constant and x would signify the hours they worked

The equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

What is a linear equation?

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

Jerald is having drain issues at his home and decides to call a plumber.

The plumber charges $35 to come to his house and $50 for every hour they work.

Let x be the number of hours:

190 = 35 + 50x

50x = 155

x = 3.1 hours

Thus, the equation to determine the number of hours worked by the plumber is 190 = 35 + 50x and the number of hours is 3.1 hours option (A) is correct.

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A local pizza shop has a membership program for frequent buyers. the membership costs $20 per month and members get a discounted price of $1.75 per slice of pizza. robert purchased a membership to this pizza shop. how much would robert have to pay the pizza shop if he bought 6 slices of pizza this month? what would be the monthly cost for xx slices of pizza?

Answers

Answer: $10.50

Step-by-step explanation:

Cot of 1 slice a pizza = $1.75

Cost of 6 slices of pizza = 6 × $1.75

=$10.50

Hence, Robert will pay $10.50 for the 6 slices of pizza and $20 for the membership.

which lines are parallel if angle 4 = angle 5? justify your answer

Answers

r and s are the parallel lines, if ∠4 equals ∠5.

Given,

The figure with,

Four lines: Line r, Line s, Line l and Line m.

Angles: ∠1, ∠2, ∠3, ∠4, ∠5, ∠6, ∠7 and ∠8

Here, we have to find the parallel lines when ∠4 = ∠5

Lets see:

Angle 1 and angle 4 are the same because the opposite angles created by two crossing lines are identical. As a result, angle 1 also equals angle 5.

The corresponding angles are identical when two parallel lines cross across a line. To put it another way, if r and s are parallel, the angles created when l intersects r and s are same. Angle 1 equals Angle 5, Angle 2 equals Angle 6, etc. We can infer that r and s are parallel since we know that angle 1 Equals angle 5.

So, we can conclude that if ∠4 equals ∠5, then r and s are the parallel lines.

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Please help me I will give you extra points and the crown

Using the figure below, Maggie used the definition of vertical angles to help her solve for x. Since vertical angles are congruent, she set the two given expressions equal to each other. After solving for x, her teacher said she got the wrong value for x. Explain where Maggie made her mistake when solving for x.

Answers

Answer:

Maggie did not combine like terms correctly when she subtracted 7x from both sides of the equation. Here is a correct solution:

4x + 2 = 7x - 25

-3x + 2 = -25

-3x = -27, so x = 9, not -9

What is the value of x, when -9 (-5) = 1 + 22-¹/?
O A x=1³
I= 1²/
O B. X= 2/1/
OC x=2²/
OD x=2³/1

Answers

I can help you with this equation, if you type it out correctly :). The input you made doesn´t make sense.

ndiba wants to buy a wagon that costs $217. how much change does he receive if he gives the cashier $250?

Answers

Answer:

change = $33

Step-by-step explanation:

ndiba wants to buy a wagon that costs $217. how much change does he receive if he gives the cashier $250?

250 - 217 = change

change = $33

{assuming no sales tax]

Frank is riding his bicycle for 6 hours at a speed of 9.6 kilometers per hour. For how many kilometers does he ride?

Answers

he rode 57.6 kilometers

-w/5 + nine = thirteen

Answers

Answer:

w=-20

Step-by-step explanation:

-w/5+9=13

-w/5=-1/5w

-1/5w+9=13

Subtract 9 on both side

Multiply both sides by -5/1

w=-20

Answer:

w=20

Step-by-step explanation
.

2/3c - 2 = 2 + c

Solve for C.

Answers

Answer:

c=-12

Step-by-step explanation:

Let's solve your equation step-by-step.

2/3c−2=2+c

Step 1: Simplify both sides of the equation.

2/3c−2=2+c

2/3c+−2=2+c

2/3c−2=c+2

Step 2: Subtract c from both sides.

2/3c−2−c=c+2−c

−1/3c−2=2

Step 3: Add 2 to both sides.

−1/3c−2+2=2+2

−1/3c=4

Step 4: Multiply both sides by 3/(-1).

(3/−1)*(−1/3c)=(3/−1)*(4)

c=−12

Answer:

c=−12

how many groups of 5/8 are in 15/16? Show all your work.

Answers

1) turn 5/8 into the same denominator

5/8 -> 10/16

2) Ignore the fractions and leave the top

10, 15

3) Divide 15 by 10

15/10 = 1.5

There are 1.5 groups of 5/8 in 15/16

surface area of a cuboid with dimensions of 9cm 5cm and 7cm

Answers

I’m not sure of the answer but this might help


Chloe had 3/4 of a pizza left. Addie ate 1/6 of Chloe's pizza. How much pizza did Addie eat?

Answers

Answer: 3/24 or 1/8 of the pizza

Step-by-step explanation:..

3/4= 9/12
1/6 = 2/12

Addie ate 2 slices from a 12 slice pizza or 2/12

On a certain hot summer's day, 273 people used the public swimming pool. The daily prices are $1.25 for children and $2.50 for adults. The receipts for admission totaled $528.75. How many children and how many adults swam at the public pool that day?

Answers

The number of children is 123 and the number of adults is 150 for that day.

According to the question,

We have the following information:

273 people used the public swimming pool.

Price for children = $1.25

Price for adults = $2.50

The total amount received = $528.75

Now, let's take the number of children to be x and the number of adults to be y on that day.

So, we have the following expression:

x + y = 273

x = (273-y) .... (1)

1.25x + 2.50y = 528.75

Now, putting the value of x from equation 1:

1.25(273-y) + 2.50y = 528.75

341.25 - 1.25y + 2.50y = 528.75

341.25 + 1.25y = 528.75

1.25y = 528.75-341.25

1.25y = 187.5

y = 187.5/1.25

y = 150

Now, putting this value of y in equation 1, we will find the value of x:

x = 273-y

x = 273-150

x = 123

Hence, the number of children is 123 and the number of adults is 150 on that particular day.

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could someone lend a hand... please?

Answers

The diagram prove that  m ║n by the consecutive interior angles converse.

How to find angles?

The diagram is to prove line m is parallel to line n.

Therefore,

m ║ n

Hence,

m∠1 = 115°, m∠2  = 65° is given.

m∠1 + m∠2 = m∠1 + m∠2 follows the reflexive property of equality.

The reflexive property of equality means that anything is equal to itself

m∠1 + m∠2 = 115° + 65° is the substitution property of equality

Supplementary angles add up to 180 degrees.

m∠1 + m∠2 = 180 is the definition of supplementary angles

∠1 and ∠2 are supplementary when simplify

m ║ n by consecutive interior angles converse.

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Someone help with geometry please the answer I put isn’t correct

Answers

The △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.

What is the congruency of triangles?Triangle congruence: If all three corresponding sides and all three corresponding angles are equal in size, two triangles are said to be congruent. Slide, rotate, flip, and turn these triangles to create an identical appearance. They are in alignment with one another when moved.

So, △ABC ≅ △DCB:

CB = CB (Common line - Given)AC = DB  (Similar lines - Given)∠ABC = ∠DCB = (Right angle - Given)

So, △ABC ≅ △DCB is under SAS condition.

Therefore, the △ABC is congruent to △DCB (△ABC ≅ △DCB) under the SAS condition.

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1. How would you subtract a negative fraction from a positive
decimal?

Answers

Answer:

you could either make the fraction a decimal or my personal like is to make the decimal a fraction

Step-by-step explanation:

convert the fraction to a decimal or decimal to fraction

3x^2 + 36x + 11 = 0

Hello, could you please help me factorise this / complete the square?

Answers

Answer:

x = +/-[tex]\frac{\sqrt{291} }{3} -6[/tex]

Step-by-step explanation:

Which of the following is the definition for permutation?
A. Selections of objects in which the order of the objects doesn't
matter.
B. The probability of an event where order doesn't matter when
selecting the objects.
C. Selections of objects in which the order of the objects matters.
D. The probability of an event where order matters when selecting
the objects.
SUBMIT

Answers

C, a way, especially one of several possible variations, in which a set or number of things can be ordered or arranged.
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