Mathematics High School

A regular octagonal pyramid. Each side of the base is 6 cm long. it has a height of 10cm. Find the surface area of the pyramid​

Answers

Answer 1

9514 1404 393

Answer:

  470.16 cm²

Step-by-step explanation:

The apothem of the base is used for two purposes: to find the area of the base, and to find the slant height of each face.

The apothem of the base for side length s is ...

  s/2 = a·tan(π/8)

  a = s/(2·tan(π/8)) ≈ 7.24 cm

The slant height of a triangular face is found using the Pythagorean theorem. The apothem of the base and the height are legs of the right triangle whose hypotenuse is the slant height. For slant height x, we have ...

  x² = 10² + a² = 100 +52.46

  x ≈ √152.46 ≈ 12.35

__

The area of the 8 triangular faces will be ...

  A = 1/2Px . . . . where P is the perimeter of the pyramid

The area of the base will be ...

  A = 1/2Pa

So, the total surface area is ...

  A = 1/2P(a + x) = (1/2)(8)(6 cm)(7.24 +12.35 cm) ≈ 470.16 cm²

Answer 2

The answer is 470.16 cm²

Related Questions

What is the value of the growth factor of the function?
A) 1/5
B) 1/3
C) 2
D) 6

Answers

Answer:

B

Step-by-step explanation:

Divide 18 by one third and see what ya get

then 6, then 2. BOOM!

Andres has $7 he needs $50 to buy a skateboard each week his grandmother pay him $4 to complete some chores

Answers

Answer:

she has to give him 4 dollars each week for 11 weeks since he already has 7 dollars.

Step-by-step explanation:

4 x 11 = 44 +7 = 51 so now he had enough for a skateboard.

ANSWER QUICK HANKS I WILL GIVE BRAINLIEST

Answers

Answer:

2 2/9

Step-by-step explanation:

Answer: 2 2/9

Step-by-step explanation:

16/9÷4/5=80/36 simp 2 2/9

A store sells a package of 25 trading hearts for $5.25 use pencil and paper explain how you can tell that the unit price per card is less than $1 what is the unit price per card.

Answers

Answer:

Unitary cost per card= $0.21

Step-by-step explanation:

Giving the following information:

Number of cards per packecge= 25

Total cost per package= $5.25

To calculate the unitary cost of each card, we need to use the following formula:

Unitary cost per card= total cost / number of cards per package

Unitary cost per card= 5.25 / 25

Unitary cost per card= $0.21



Team Damon or team Stefan Or team Kai I’m team ✨Damon✨and ✨Kai✨all the way

Answers

Damon, Kai and klaus
I am team Damon and Kai

Please help, I'm stuck...

it looks so simple yet I don't get how to do it. Can anyone help explain?

(picture of question attached)
source: Pearson/Savvas Realize​

Answers

I’m not sure but keep trying

Whats the answer pls help

Answers

Answer:

The area of the lateral surface of the cube is 12.96 cm²

Step-by-step explanation:

The lateral surface area

4 × (1.8 cm)²

An objects lateral surface are the surfaces of the object that exclude the top and bottom surfaces

In a cube, the lateral surface are the vertically oriented (with respect to the base and the top which are then oriented horizontally) surfaces of the cube

Therefore, the lateral surface area of the cube consist of four vertically oriented equal sized faces, each with side 1.8 cm

The area of the lateral surface of the cube = The area of the four vertically oriented faces of the cube

∴ The area of the lateral surface of the cube = 4 × 1.8 cm × 1.8 cm = 12.96 cm.²

solve for x:
x/2 + x/5 = 1

Answers

Answer:

x=10/7

Step-by-step explanation:

Answer:

X= 10/7

Step-by-step explanation:

I hope this works

HELP PLEASE :( thank u

Answers

I really don’t know but I’m sure it’s the 1

Find the GFC of 16 and 80

Answers

Answer:

It is 16

Step-by-step explanation:

Hope this helped have an amazing day/month/year!

PLEASE PLEASE HELP I STG IVE BEEN ASKING THE SAME QUESTIONS FOR SO LONG AND NOONES ANSWERING ITS DUE SOON im just gonna fail tbh

Answers

Answer:

3) 5/2

Step-by-step explanation:

5x - 2y = 20

(First, put it in slope intercept form: y = mx + b).

5x - 2y - 5x = 20 - 5x --> Subtracted 5x on both sides of the equation

- 2y  = -5x + 20 --> Simplified

-2y/-2 = (-5x + 20)/-2 --> Divided by -2 on both sides

y = 2.5x - 10 --> Simplified

Since formula is, y = mx + b, then:

m (slope): 2.5

b (y-intercept): -10

Therefore, the answer is 3) 5/2

Hope this helped! <3

Let's solve for y.

5x − 2y = 20

Step 1: Add -5x to both sides.

5x−2y+−5x=20+−5x

−2y=−5x+20

Step 2: Divide both sides by -2.

−2y/−2  =  −5x + 20/−2

y =  5/2x − 10

Answer:

y =  5/2x − 10

Slope = x, therefore, the slope = 5/2.

Last year a bag of Farmer Bill's seed corn cost $140. This year that price has increased by 60%. How much will a bag of seed corn cost Farmer Bill this year? *

Answers

Your answer would be $84

Solve the inequality. Please help answer needed fast!! Will give BRAINIEST ANSWER 10 POINTS!!!

Answers

Answer:

lol

edited: x is negative

Step-by-step explanation:

Evaluate the expression.

−4(−2) − 4 − 2 =

Answers

Answer:

2

Step-by-step explanation:

-4 x -2 is 8. -4 -2 is -6. 8-6 is 2.

Answer:

8-4-2=2

It was +8 because the multiplication of two negatives will give u a positive

Step-by-step explanation:

Tess studied for 2/3 of an hour on Monday and 1 1/2 hours on Tuesday. How much more time did she spend studying on Tuesday than on Monday?

Answers

Answer:

she spent  2 1\6 studying more on tuesday because you got to add

In ΔQRS, the measure of ∠S=90°, the measure of ∠Q=54°, and RS = 26 feet. Find the length of QR to the nearest tenth of a foot

Answers

SOH-CAH-TOA

sin Q     =    Opposite     =    26

                 hypotenuse          x

sin 54   =     26

                     x

x sin 54 = 26

x sin 54      =         26    

sin 54                sin 54

x =        26      =    32.1378  ≈  32.1 feet

          sin 54


What is the slope of the line shown below?

(3,9)

(-4,2)

Answers

Answer:

the slope of the line shown below is 1.

3(-1 - x) < -20 - 3x
on a number line

Answers

Answer:

[tex] - 3 - 3x \: < \: - 20 - 3 \\ - 3x < - 20 - 3 + 3 \\ - 3x < - 20 \\ x > - 20 \div 3[/tex]

Help plz I’m giving a lot of points

And no nonsense answers plz

Answers

Answer:

it is a positive number because she was rising if she had been going down then the number would have become negative.

Step-by-step explanation:

it is a positive number because she was rising,

however, if she was going down the number would become negative.

Please help me complete this !! 12points

Answers

Answer:

1.

x1=1

x2=3

y1=5

y2=1

midpoint= (x1+x2/2, y1+y2/2)=(1+3/2,5+1/2)=(2,3)

2.

x1=2

x2=4

y1=4

y2=6

midpoint= (x1+x2/2, y1+y2/2)=(2+4/2,4+6/2)=(3,5)

3.

x1= -2

x2=4

y1=4

y2= -6

midpoint= (x1+x2/2, y1+y2/2)=(-2+4/2,4-6/2)=(1,-1)

4.

x1=0

x2=0

y1=3

y2=5

midpoint= (x1+x2/2, y1+y2/2)=(0/2,3+5/2)=(0,4)

5.

x1= -2

x2=2

y1= -6

y2=6

midpoint= (x1+x2/2, y1+y2/2)=(-2+2/2,-6+6/2)=(0,0)

6.

x1=1

x2=4

y1=4

y2=5

midpoint= (x1+x2/2, y1+y2/2)=(1+4/2,4+5/2)=(5/2,9/2)

7.

x1=-3

x2=-4

y1=5

y2=5

midpoint= (x1+x2/2, y1+y2/2)=(-3-4/2,5+5/2)=(-7/2,5)

8.

x1=5

x2= -4

y1=2

y2=6

midpoint= (x1+x2/2, y1+y2/2)=(5-4/2,2+6/2)=(1/2,4)

Equivalent expression for m-(8-3m)

Answers

Answer:

4m-8

Step-by-step explanation:

answer

Answer:

4m - 8

Step-by-step explanation:

Given expression,

→ m - (8 - 3m)

Simplifying the expression,

→ m - (8 - 3m)

→ m - 8 + 3m

→ 4m - 8

→ 4(m - 2)

Hence, answer is 4m - 8.

which expression are equivalent to 2(4f+2g)​

Answers

Answer:

8f+4g

Step-by-step explanation:

solve for x.

3x - 8x + 2 = 17

X=

Answers

Answer:

-3

Step-by-step explanation:

3x-8x=17-2

3x-8x=15

-5x=15

-x=15/5

-x=3

x=-3

Kate saved each week for 5 weeks and then spent $25. How much was she saving each week if she had $100 left at the end of 5 weeks and after spending $25? /3

Answers

Answer:

25 a week.

Step-by-step explanation:

100+25= 125

125÷5 = 25

Solve m+4>9

The solution is __

Answers

Answer:

m>5

Step-by-step explanation:

Answer:

m > 5

Step-by-step explanation:

m+4>9

m > 9 - 4

m > 5

or

m ∈ 《5 , +∞》

If a new surfboard in North Carolina costs $320 and the sales tax is 4.75%, what
was the total cost of the surfboard?
$335.20
$304.80
$321.25
$342.40

Answers

$320 + 4.75% = $15.20 .

$320+$15.20= $335.20

how do you solve this
(-4) + (+6)

Answers

Answer:

2

Step-by-step explanation:

-4+6=

6-4=

2

The answer is positive 2

YOU GUYS ARE MEAN! AND AREN’T HELPING ME AND IM WILLING TO GIVE 40POINTS! LOOK AT THE PICTURE ATTACHED!

Answers

Answer:

[tex]x = 5[/tex]

Step-by-step explanation:

[tex] {2}^{2x - 3} + 52 = 180[/tex]

[tex] {2}^{2x - 3 } = 128[/tex]

[tex] {2}^{2x - 3} = {2}^{7} [/tex]

[tex]2x - 3 = 7[/tex]

[tex]2x = 10[/tex]

[tex]x = 5[/tex]

1/2=2m then what is m?

Answers

Answer:

m = 1/4 or 0.25

Step-by-step explanation:

1/2 = 2m

[Symmetric property of equality]

2m = 1/2

÷2. ÷2

[Division property of equality]

m = 1/2 ÷ 2

m = 1/4

________

1/2 = 2m → 1/2 = 2(1/4) → 1/2 = 2/4 →

1/2 = 2÷2/4÷2 → 1/2 = 1/2

this is the choices
88
70
110
120

Answers

Answer would be 110 because if a figure has 4 angles all it's angle lengths add up to 360°, so since one of the angles is 70° and there is another angle that's identical to it, 70+70= 140, so you have to do 360-140 which gives you 220, and 220/2 = 110°

Answer:

110

Step-by-step explanation:

as a trapezoid contains of angles that add up to 360 .....and the top angles are equal and the bottom angles are equal ...therefore >v equals to 70 and w as well and x are equal to 110 each

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