6. Find the surface area of the regular pyramid shown to the nearest whole number. The figure is (1 point)
not drawn to scale.
11 m
12 m
6√3
01,540 m²
0770 m²
0396 m²
0749 m²
Answers
Area of hexagon
6(1/2BH)3BH3(6√3)(12)216√3m²Now
area of upper 6 triangles
3BH3(11)(12)396m²Total area
396+216√3770.112m²770m²Answer:
770 m²
Step-by-step explanation:
The surface area of a regular pyramid comprises the area of the base (regular polygon) and the area of each of the slanted sides (triangles).
Apothem: The line segment from the center of the regular polygon to the midpoint of one of its sides.
Area of the base
The base of the prism is a regular polygon with 6 sides (hexagon).
[tex]\textsf{Area of a regular polygon}=\sf \dfrac{1}{2}nsa[/tex]
where:
n = number of sidess = side lengtha = apothemGiven:
n = 6s = 12 ma = 6√3Substitute the given values into the formula:
[tex]\begin{aligned}\implies \textsf{Base area}& =\sf \dfrac{1}{2}\cdot 6 \cdot 12 \cdot 6\sqrt{3}\\ & = \sf 216\sqrt{3}\:m^2\end{aligned}[/tex]
Area of one side
The sides of the regular pyramid are congruent triangles.
[tex]\textsf{Area of a triangle} = \sf \dfrac{1}{2} \times base \times height[/tex]
Given:
base = 12 mheight = 11 mSubstitute the given values into the formula:
[tex]\implies \textsf{Area of a triangle} = \sf \dfrac{1}{2} \times 12 \times 11=66\:m^2[/tex]
Total Surface Area
[tex]\begin{aligned}\implies \textsf{Total Surface Area} & = \sf base \: area + 6 \times side \: area\\& = \sf 216\sqrt{3}+6 \cdot 66\\& = \sf 216\sqrt{3}+396\\& = \sf 770\:m^2\:(nearest\:whole\:number)\end{aligned}[/tex]
Related Questions
The sum of two numbers is 36. One number is 2 times as large as the other. What are the numbers?
Larger number:
Smaller number:
Answers
Let the first number be "x", and the 2nd number (which is twice as large as the other), be 2x.
Set the equation
2x + x = 36
Simplify. Combine like terms
(2x + x) = 36
3x = 36
Isolate the x. Divide 3 from both sides
(3x)/3 = (36)/3
x = 36/3
x = 12
The first number is 12
The second number is 2x. Replace x with 12. Multiply.
2x = 2(12) = 24
The second number is 24
Check: 12 + 24 = 36 (True)
Answer: 12 & 24
Select the correct answer. what is the y-intercept of f(x) = 3x 2? a. (9,0) b. (0,9) c. (0,-9) d. (9,-9)
Answers
The y-intercept of a line is the point where the line cuts the y-axis or the point where x = 0. The y-intercept of the line with the function y = 3x + 2 is (0, 2)
Intercept of a lineThe y-intercept of a line is the point where the line cuts the y-axis or the point where x = 0.
Given the equation of a line f(x) = 3x +2
If x = 0, them;
f(0) = 3(0) + 2
f(0) = 2
Hence the y-intercept of the line with the function y = 3x + 2 is (0, 2)
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Answer:
answer is (0, 9)
Step-by-step explanation:
did the test. plato.
ur welcome buddy
What is 6 3/4 % of $7,600.00
A. 513
B. 520
C. 456
D. 479.25
E. 550
Answers
Answer:
A 513
Step-by-step explanation: is your answer
Hope this helps :)
find two numbers who's difference is 10 and 1/6 of whose sum is 11
Answers
Answer:
38 and 28
Step-by-step explanation:
let the 2 numbers be a and b
(a - b)= 10.................................................1
1/6(a + b) = 11
hence (a + b) = 66...................................2
adding 1 and 2
a -b + a + b = 10 + 66
2a=76
a = 38
b=28
Can anyone tell me the formula or way to solve this problem
Answers
[tex]\text{It is an equilateral triangle, so all angles are equal to}~ 60^{\circ}\\\\~~~~~~m\angle 2 = x+72\\\\\implies 60 = x+72\\\\\implies x = 60-72\\\\\implies x = -12[/tex]
A bicycle store costs $2200 per month to operate. The store pays an average of $40 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even?
Answers
Answer:
Step-by-step explanation:
120n=2400+60n is break-even point
60n=2400
n=40 bikes need to be sold monthly to break even!!!!!!!!!!!!
Find the area of the green triangle
Answers
Answer:
if im correct the answer is 48 ft2
Step-by-step explanation:
Answer:
[tex]16ft \: ^{2} [/tex]
Step-by-step explanation:
To find the area of the given triangle we'll use the formula:-
[tex]\boxed{\sf A = \cfrac{1}{2} \times b \times h}[/tex]
Where,
Base(B):- 8 ftHight (H):- 4ft[tex]\sf A = \cfrac{1}{2} \times 8 \times 4[/tex]
First, let's multiply 1/2 * 8 = 8/2.
[tex]\sf \cfrac{8}{2} \times 4[/tex]Divide 8 by 2= 4
[tex]\sf 4 \times 4[/tex][tex]\sf 16[/tex]Thus, the area of the triangle is 16ft^2.
i don't know exactly what to do
Answers
Answer:
Step-by-step explanation: Just relax effortlessly. Communion Kant be for All unless we are primed for purpose...
The element silicon has a molar mass of 28.09 g/mol. Calculate the mass of 0.15 mol of Silicon.
Answers
The answer is 28.09 g. I hope this helped.
Answer:
The answer is 4.2 g
The circumference of a circle is 18π, what is the radius?
Answers
Answer: 9
Explanation: Because pi is included in the answer, you won't be multiplying pi with it.
The only number that equals to 18 is 9.
By using the formula for circumference is: 2πr
2 x 9 = 18
Add pi, 18π.
This pattern follows the rule multiply by 2. what other feature do you observe? 4, 8, 16, 32, 64, 128
group of answer choices
all terms are even because even x even = even.
all terms are odd because even x even = odd.
all terms are even because odd x odd = even.
all terms are even because odd x even = even.
Answers
Answer:A. All terms are even because even x even = even.
Step-by-step explanation:Hope It helps you have a good day.
he tables represent the functions f(x) and g(x). A table showing g(x) equals 2 x plus 15 with 2 columns and 7 rows. The first column, x, has the entries, negative 15, negative 12, negative 9, negative 6, negative 3, 0. The second column, g(x), has the entries, negative 15, blank, blank, blank, blank, 15. Which input value produces the same output value for the two functions? x = –12 x = –9 x = –6 x = –3
Answers
Answer:
Answer:
C
Step-by-step explanation:
Answer:
x=-6
Step-by-step explanation:
i got a hundred on the test
25(-7)= ?
what type of equation is this?? division, multiplication, addition, or subtraction??
Answers
Answer:
multiplication
Step-by-step explanation:
the () means to multipy
Someone pls do this for me I give Brainly
Answers
Answer:
Kindly read through
Step-by-step explanation:
All have been solved step by step
I need help! Find the measure of the indicated angle to the nearest degree.
Answers
Answer:
30
Step-by-step explanation:
let unknown angle = x
cos = adjacent / hypotenuse
adjacent of ? = 13
hypotenuse = 15
cos(x) = (13/15)
==> take inverse cos of both sides
x = 30 (rounded)
Note : hypotenuse = longest side and adjacent = side thats not the hypotenuse or opposite
Triangle r q s is cut by line segment t v. line segment t v goes from side q r to side r s. the length of r v is x 10, the length of v s is x, the length of r t is x 4, and the length of t q is x minus 3. which value of x would make line segment t v is parallel to line segment q s? 3 8 10 11
Answers
The value of x that would make line segment T V is parallel to line segment Q S is where x = 10. (Option C)
What is a line segment?In Mathematics, a Line Segment is a part of a line that has two endpoints.
The difference between a line segment and a line is that while the former has a starting and an endpoint, the latter does not. See the attached image.
What is the Step by Step solution to the above problem?Step 1
Note that if QS is Parallel to TV, then both sides of the triangle must be proportionally divided by TV.
That is: RV/VS = RT/TQ.
Step 2 - replace the segments by the relevant equations
(X + 4)/(X- 3) = (X+10)/(X)
Step 3 - Cross Multiply
x(x +4) = (x -3)(x +10)
Removing the parentheses, we have
X² +4X = X² +7X -30; Subtract X² from both sides and we have;
4X = 7X - 30
Step 3 - Collect like terms by cross multiplying-3X = -30 or
3X = 30
Divide both sides by three and we have:
X = 10
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Answer:
10 is the answer
HALPPPP its a drop-down
Answers
Answer:
Wider than4 units down565.948063818 to 1 decimal place.
Answers
Answer:
565.9.
Step-by-step explanation:
The second decimal place is 4 so the first one stays at 9.
Is the vertex of the graph a maximum or a minimum?
Answers
Answer:
maximum
Step-by-step explanation:
the vertex will give the maximum value for y, which is 3
Is it more reasonable to say that a pen weighs 2 ounces, 2 pounds, or 2 tons?
Answers
Answer:
2 ounces
Step-by-step explanation:
2 pounds and 2 tons are a lot of weight to assume the weight of a pen.
which object is 3 1/2 inches loong
Answers
Answer:
ur mom
Step-by-step explanation:
expirence and funnes
Answer:
yello
Step-by-step explanation:
the yellow one
Geri built a pencil box in the shape of a right rectangular prism. the amount of space inside of the box is 176 cubic inches. what is the height of geri’s pencil box? a rectangular prism with a length of 8 inches, width of 11 inches, and height of question mark. 2 inches 4 inches 8 inches 9 inches
Answers
The height of the pencil box is 2 inches
How to determine the height of the pencil box?The given parameters are:
Volume = 176
Length = 8
Width = 11
The height of the pencil box is calculated using
Height = Volume/(Length * Width)
So, we have:
Height = 176/(8 * 11)
Evaluate
Height = 2
Hence, the height of the pencil box is 2 inches
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Answer:
2 Inches
Step-by-step explanation:
Good Luck
(2y + 5) (5y + 7)
Simplify your answer.
Answers
Answer:
10y^2 + 39y + 35
Step-by-step explanation:
Simplify using FOIL
please help i dont get it... (average rate of change)
10.
The graph shows the price, in dollars, of a new digital toy for different levels of supply.
(image provided)
What is the average rate of change?
Answers
Answer:
-3
Step-by-step explanation:
Formula for average rate of change :
A(x) = f(a) - f(b) / a - bSolving :
A(x) = 115 - 85 / 5 - 15A(x) = 30/-10A(x) = -3You start at (3, -2). You move up 5 units. Where do you end?
Answers
Answer:
You would end at (3, 3).
Explanation:
You would plot your first mark at 3 on a typical xy graph because the first number in ()'s is always x (horizontal line).
Second, because your second mark is y (vertical line), you would plot -2 on the vertical axis.
Your y plot would be 5 more than -2 because you're traveling up five units, giving you (3, 3).
Explanation: you would end up at (3, 3) because you are originally given (3, 2) and the order goes (x, y). x is the placement on the horizontal line when y is the placement on the vertical line. So since you are starting at 3 to the right and 2 below zero you would move up 5 and get to (3, 3). :)
The resources used in the production of goods and services are limited so society must
Answers
Society must use the resources wisely without wasting any good.
What are resources?The products and the services of daily use in the life of the human being are called the resources. It can be anything like a toothbrush, clothes, electronic products etc.
The basic necessity of human is food, water and electricity we must use them wisely because of the continuous increase in the population on th earth the resources are also decreasing. So we should not waste them unnecessarily.
Therefore Society must use the resources wisely without wasting any good.
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im rlly frickin lost
pls help
Answers
Answer:
so far he has saved 27 dollars however he needs 33 more dollars
Step-by-step explanation:
okay so if it says "____ of x" you normally have to multiply (of is a hint)
so first lets see how much he saved
0.45(60) = 27
he saved 27 dollars so far. to find how much more he has to save, you have to do the amount he needs minus the amount he already has
sooo
60 - 27 = 33
uhhh im not sure what the graph table thing on the right is, but i hope this helps a little
edit: ohhhhh so in the table all you have to do is fill in the information. im sure u can do it, but if you still dont know how to just reply here and ill help!
Choose all the equations that are equivalent
to -3(x - 2) = 4x − 2(x - 1).
-
Enter the corresponding letters, in alphabetical
order, separated by commas (without spaces).
A. -5x = -4
B. -5x = 4
C. -5x = 8
D. 2x - 4 =-3x
E. -3x + 6 = 2x + 2
F. -3x - 6 = 2x - 2
Answers
Answer:
a,e
Step-by-step explanation:
Answer:
A, E
Step-by-step explanation:
lets first solve the equation using distributive property:
-3(x-2)=4x-2(x-1)
-3x+6=4x-2x+2
-3x+6=2x+2 (E)
Now move the like terms on one side:
-3x-2x=2-6
-5x=-4 (A)
Does anyone know the length the height and the width of this object and also Based on the above values, the volume of the object ? pls someone help me
Answers
What is ∑n=15[5(−2)n−1] equal to?
Answers
Answer:
Although the notation is sloppy, I will assume based on former questions of the same that "∑n=15[5(−2)^n−1]" translates mathematically to . Please correct me, though, if this in incorrect.
Anyway, there is neat formula that will deal with question very quickly. It is the following:
Sn is the sum of the geometric series
a1 is the first term in the series
r is the common ratio
n is the number of terms in the finite geometric series
Let's use this formula to our advantage! However, there are two variables that we do not know: a1 and n. Let's start with a1.The first term in the series is when n=1, so let's determine what that is.
The expression ∑n = 15 [5 (−2) n − 1] is equal to 5/16384.
What is an expression?An expression contains one or more terms with addition, subtraction, multiplication, and division.
We always combine the like terms in an expression when we simplify.
We also keep all the like terms on one side of the expression if we are dealing with two sides of an expression.
Example: so
1 + 3x + 4y = 7 is an expression.com
3 + 4 is an expression.
2 x 4 + 6 x 7 – 9 is an expression.
33 + 77 – 88 is an expression.
We have,
First, let's understand the notation.
∑n = 15 represents the sum of the expression that follows for n starting from 15, and the expression is 5 (−2) n − 1.
So, we need to find the sum of 5 (−2) n − 1 from n = 15 to n = 15, which means there is only one term in the sum.
Substituting n = 15, we get:
5 (−2) (15 − 1) = 5 (−2) 14 = 5/16384
Therefore,
The expression ∑n = 15 [5 (−2) n − 1] is equal to 5/16384.
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