Find the surface area and lateral area of the following three prisms. Be sure to show all of your work.
Problem 1
L = 10 = length
W = 5 = width
H = 4 = height
SA = surface area of a rectangular prism, aka block or box
SA = 2*(LW+LH+WH)
SA = 2*(10*5+10*4+5*4)
SA = 220
--------------------
LA = lateral area, aka wall area
LA = (perimeter of the base)*(height)
LA = (2L+2W)*H
LA = (2*10+2*5)*4
LA = 120
or
LA = SA - (floor area) - (ceiling area)
LA = SA - 2*(area of the floor)
LA = 220 - 2*(LW)
LA = 220 - 2*(10*5)
LA = 220 - 100
LA = 120
--------------------
Answers:
Surface Area = 220 square feet
Lateral Area = 120 square feet
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Problem 2
Imagine rotating the object so that the triangular face is resting on the flat ground. This means the triangular faces are the floor and ceiling. The walls of any prism are always rectangles.
Focus on the right triangle with leg b = 4 and hypotenuse c = 5.
Use the pythagorean theorem to find that a = 3 is the missing leg length.
The triangle has base = 4 and height = 3, so its area is base*height/2 = 4*3/2 = 6 square inches. This is the area of the floor and ceiling each.
--------------------
This is the summary so far
base or floor area = 6 square inchesdepth of the prism = 8 inches(a,b,c) = (3,4,5) are the sides of the right triangleThose values are then plugged into the formulas below.
SA = surface area of a triangular prism
SA = 2*(base area) + depth*(a+b+c)
SA = 2*(6) + 8*(3+4+5)
SA = 108
LA = lateral area
LA = depth*(a+b+c)
LA = 8*(3+4+5)
LA = 96
or
LA = SA - 2*(floor area)
LA = 108 - 2*(6)
LA = 96
Note that a+b+c = perimeter of the triangular base.
--------------------
Answers:
Surface Area = 108 square inches
Lateral Area = 96 square inches
==========================================================
Problem 3
Imagine rotating the figure so that the octagon is resting on the flat ground.
Refer to the screenshot below to see the steps on computing the area of the regular octagon, aka the floor area.
The floor area is approximately 120.710678 square cm. The same goes with the ceiling because the floor and ceiling are congruent regular octagons that are parallel.
Each rectangular wall has an area of 5*22 = 110 square cm. Eight identical walls give a total lateral area of 8*110 = 880 square cm.
Add the floor and ceiling area to the wall area to get the total surface area
floor + ceiling + walls = 120.710678 + 120.710678 + 880 = 1121.421356
--------------------
Answers:
Surface Area = 1121.421356 square cm (approximate)
Lateral Area = 880 square cm
Please Help Giving Brainlist!!!!! Given that the area of rectangle IJKL is 490 units^2, what are its length and width?
Answer:
Option 4
Step-by-step explanation:
Equating given length and width to the area :
8x(5x) = 49040x² = 490x² = 490/40x² = 12.25x = 3.5Finding the dimensions :
length = 8x = 8(3.5) = 28 unitswidth = 5x = 5(3.5) = 17.5 unitsWill mark brainliest for right answer
Check all statements that are true. If none are true click “None”
A- Since it is a repeating decimal, 14.19 is irrational.
B- Since it is a terminatingdecimal, 12.19 is rational.
C- Since 16 is a perfect square,
16 is irrational
D- Since 6 is not a perfect square, 6 is rational.
E- Since it’s a ratio of two integers 11/3 is rational
Answer:
B and E are True.
Step-by-step explanation:
B 12.19 is a terminating decimal so it is rational.
E its a ratio of 2 integers so its rational.
A - is not repeating so this is false.
C. a perfect square is rational - 16 can be written as 16/1.
D. 6 is rational because it can be written as 6/1 not because its not a perfect square.
please please please help help help !!
Answer:
The axis of Symmetry divides a line into two equal halves.
Step-by-step explanation
An easy relation to get this value without plotting a graph is x = –b/2a
Where
a = coefficient of x²
b = coefficient of x
From the Question, We need a symmetry of value –½
The only Option that'll give this value is OPTION D
2x – y = 5 – 2x²
Since its a line, Don't forget to make "y" subject before doing any operation.
y = 2x² + 2x – 5
a = 2
b= 2
x = –(2)/2(2)
= –2/4
= –½
Julianna has thirty two pieces of candy in a candy jar. Julianna only has two kinds of candy.
jolly rangers and twix. For every four twix bars, she has two pieces of jolly rangers. How many
pieces of each candy are in the candy jar?
The number of jolly rangers candy she has is 22. The number of twix bars she has is 11.
What are the linear equations that represent this question?
j + t = 33 equation 1
4t = 2j
j = 2t equation 2
Where:
j = number of jolly rangers
t = j = number of twix
How many twix candies does Julianna have?
Substitute for j in equation 1 using equation 2
2t + t = 33
3t = 33
t = 11
How many jolly candies does Julianna have?Subsitute for t in equation 2
j = 11 x 2 = 33
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Please help asap
trevon is helping his sister study for her geometry test while staying at a hotel.
how can trevon use the hotel's third floor, sixth floor, and the elevator to illustrate the concepts of parallel and perpendicular?
a.
the hotel floors are perpendicular to each other, and the elevator moves in a path that is parallel to them both.
b.
the hotel floors are perpendicular to each other, and the elevator moves in a path that is perpendicular to them both.
c.
the hotel floors are parallel to each other, and the elevator moves in a path that is perpendicular to them both.
d.
the hotel floors are parallel to each other, and the elevator moves in a path that is parallel to them both.
She should fart 10 times
I tried my best!!!! Hope this helps :D
Multiply.
[tex]\frac{\sqrt{2}}{6}cis (\frac{3\pi }{5})[/tex]·[tex]\frac{\sqrt{6}}{4}cis (\frac{2\pi }{3})[/tex]
A.[tex]\frac{\sqrt{3}}{12}cis(\frac{19\pi }{15})[/tex]
B. [tex]\frac{\sqrt{3}}{12}cis(\frac{2\pi }{5})[/tex]
C. [tex]\frac{\sqrt{2}}{8}cis(\frac{2\pi }{5})[/tex]
D. [tex]\frac{\sqrt{2}}{8}cis(\frac{19\pi }{15})[/tex]
Multiply the moduli and add the arguments:
√2/6 cis(3π/5) × √6/4 cis(2π/3)
= (√2/6 × √6/4) cis(3π/5 + 2π/3)
= √3/12 cis(19π/15) … [A]
The area of a rectangle is 48 cm². If its width is 6 cm, what is its length?
================================
[tex] \large \sf \underline{Question:}[/tex]
The area of a rectangle is 48 cm². If its wdth is 6 cm, what is its length================================
[tex] \large \sf \underline{Answer:}[/tex]
[tex] \qquad \qquad \qquad \huge \bold{8cm}[/tex]
To solve for the area of rectangle, you use this formula A = length × width. But we're doing it reversal, we will divide the width to the area
[tex]\large\tt{A \: = \: l \: \times \: w}[/tex][tex]\large\tt{48cm^{2} \: = \: l \: \times \: 6cm}[/tex][tex]\large\tt{48cm^{2} \: \div \: 6cm \: = \: l}[/tex][tex]\large\tt{48cm^{2} \: \div \: 6cm \: = \: \pmb{8cm}}[/tex]Therefore, The length is 8cm.
================================
Hey ! there
Answer:
Length of rectangle is 8 cm .Step-by-step explanation:
In this question we are provided with a rectangle having area 48 cm² and width 6 cm . We are asked to find the length of rectangle .
We know that ,
[tex] \qquad \qquad\underline{\boxed{\frak{Area_{(Rectangle)} = l \times w}}}[/tex]
Where ,
l refers to Lengthw refers to WidthSOLUTION : -
We are finding value of length by substituting value of width as 6 cm and area as 48 cm² in the formula . So ,
[tex] \quad\longmapsto \qquad \:48 = 6 \times l[/tex]
or ,
[tex] \quad\longmapsto \qquad \:48 = 6l[/tex]
Dividing with 6 on both sides :
[tex] \quad\longmapsto \qquad \: \cancel{\dfrac{48}{6}} = \dfrac{ \cancel{6}l}{ \cancel{6}} [/tex]
We get ,
[tex] \quad\longmapsto \qquad \: \orange{\underline{\boxed{ \frak{l = 8 \: cm}}}} \quad \bigstar[/tex]
Henceforth , Length of rectangle having area 48 cm² and width 6 cm is ❝ 8 cm ❞Verifying : -
We are verifying our answer by substituting value of length and width in formula and equating it with given area . So ,
[tex] 8 \times 6 = 48[/tex][tex]48 = 48[/tex][tex] \rm{L.H.S = R.H.S}[/tex][tex] \rm{Hence , \: Verified .}[/tex]Therefore , our answer is correct .
#Keep Learningfind the value of each of the lettered angles in the diagram below
Answer:
Angle a = 114 Angle b = 114 Angle c = 66 Angle d = 66
Step-by-step explanation:
180 - 48 = 132
132/2= 66
180 - 66 = 114
The parent cosine function is transformed to create the function . which graphed function has the same amplitude as function m?
Based on the graph given, the option that will show the same amplitude as function m is graph D.
Which graphed function is this about?The cosine function is seen as:
f(x) = A*cos(kx) + M
And the functions are:
A stands for amplitude, k is angular frequency,M is the midline.When the function is m(x) = -2*cos(x+π).
The absolute value of the amplitude will be 2*|-2| = 4
Therefore, the option that can have the requirement above is graph D.
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What is the solution to this equation?
log4(x^2+1)= log4 (-2x)
A.no solution
B.x = 1
C.x = -1
D. X=2
Answer:
C. x = -1
Step-by-step explanation:
Here :
log 4 (x² + 1) = log 4 (-2x)
Then :
x² + 1 = -2x
x² + 2x + 1 = 0
(x + 1)² = 0
x + 1 = 0
x = -1
A wire of length 4x is bent into the shape of a circle. A. Express the circumference of the circle as a function of 4x. B. Express the area of the circle as a function of 4x.
The circumference of the wire is 4x and the area of the circle is 4x^2/π
How to determine the circumference?The length of the wire is given as;
Length = 4x
This represents the circumference.
Hence, the circumference of the wire is 4x
How to determine the area?In (a), we have:
Circumference = 4x
Calculate the radius using:
2πr = 4x
Divide through by 2π
r = 2x/π
The area is:
Area = πr^2
This gives
Area = π(2x/π)^2
Evaluate
Area = 4x^2/π
Hence, the area of the circle is 4x^2/π
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Tasha has foam blocks stored in a box that measures 214 ft long by 2 ft wide by 2 ft tall.
Each foam block is a cube with 12ft edge length.
How many blocks can fit into the box?
8(90x6)+9(7+4) and it hard for me bec i in the 3-4 grade
Answer:
720[tex]x^{6}[/tex]+99
Step-by-step explanation:
ICE CREAM For Exercises 5 and 6, use the
following information provided in the
table.
Toppings
Ice Cream (Scoop)
Sprinkles
Hot Fudge
Whipped Cream
Nuts
Cost
x dollars
$0.25
$0.75
$0.50
$0.35
5. Ten kids each order a scoop of ice
cream. Five of the kids add sprinkles,
3 add nuts, and 2 add nothing extra.
Write and simplify an expression that
represents the total cost.
So, the simplified expression that represents the total cost is 8(x + 0.34375) dollars.
What is cost?Let x be the cost of one scoop of ice cream without any toppings. Then the total cost for each kid who adds sprinkles is x + 0.25, the total cost for each kid who adds nuts is x + 0.35, and the total cost for each kid who adds nothing extra is x.
Therefore, the total cost for the 10 kids is:
5(x + 0.25) + 3(x + 0.35) + 2x = 8x + 2.75
Simplifying this expression, we get:
8x + 2.75 = 8(x + 0.34375)
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19. Solve the following inequality.
Answer:
c
Step-by-step explanation:
(5y - 1) = 4y + (9y - 4) = 5y
2y > .75
Answer:
C. The solution set is {y|y > 0.75}.
Step-by-step explanation:
Given :
5y - 1 < 9y - 4Add 4 to each side.
5y - 1 + 4 < 9y - 4 + 45y + 3 < 9ySubtract 5y from each side.
5y + 3 - 5y < 9y - 5y4y > 3y > 3/4y > 0.75Solution set
C. The solution set is {y|y > 0.75}.
I am thinking of a number. I subtract 10 then divide by 2 and now have 19 what was my original number
Answer:
x=48
Step-by-step explanation:
(x-10)÷2=19
x-10 =19
2
(x-10)×2 =19×2
2
x-10=19×2
x-10=38
x=38+10
x=48
Solve for the exact values of x and y.
x =
y =
Answer:
Here is the solution...hope it helps:)
-(6)³;(-6)³
what is the answer to this?
Answer:
Step-by-step explanation:
-(6)³=-6×6×6=-216
(-6)³=(-6)×(-6)×(-6)=-216
it takes 3 painters 6 days to complete a job work out how many days would it take 2 painters to complete the same job (2 marks)
Answer:
t = 8 days i saw it on a website if i recall its the answer
Step-by-step explanation:
speed = distance/time
4 P = 1 House / 10 Days
P = 1 House / 40 Days
Let T = Time it takes for five painters.
5 P = 1 House / T
5(1/40) = 1 /T
1/8 = 1 /T
T = 8 Days
What are Nilpotent groups?
Answer:
that is your answer hope this helps u
!!!!!!ANSWER!!!!!!
An acute triangle has two sides measuring 8 cm and 10 cm. What is the best representation of the possible range of
alues for the third side, s?
2< s < 18
!!!!!!! 6
Os<2 ors > 18
s< 6 or s> 12.8
Answer:
1st option
Step-by-step explanation:
given 2 sides of a triangle then the third side s is in the range
difference of 2 sides < s < sum of 2 sides , that is
10 - 8 < s < 10 + 8
2 < s < 18
(9x^2+5x^2+11x)+(-2x^3+9x-8x^2)
Answer:
First step is to remove those unnecessary brackets :[tex] \longrightarrow\tt \: 9 {x}^{3} + 5 {x}^{2} + 11x - 2 {x}^{3} + 9x - 8 {x}^{2} [/tex]
Combine the like terms :[tex] \longrightarrow \tt \: 9 {x}^{3} - 2 {x}^{3} + 5 {x}^{2} - 8 {x}^{2} + 11x + 9x[/tex]
[tex] \longrightarrow \boxed{\tt \: 7 {x}^{3} - 3 {x}^{2} + 20x}[/tex]
Our final answer is 7x^3 - 3x^2 + 20x .--------- HappY LearninG <3 --------
4. At a local print shop, 25 copies cost $1.50. At this rate, how much would 60 copies cost?
Answer:
60 copies would cost 3.60
Step-by-step explanation:
Please help me with Proportions
Answer:
Step-by-step explanation:
7. Hours Money earned
4 34
8 68
10 85
14 119
8. Seconds yards
1 9
3 27
6 54
10 90
9. Minutes Cost
5 $1.50
12 $3.60
24 $7.20
30 $9.00
PLEASE HELP!!! NEED QUICKLY!!! WILL GIVE EXTRA POINTS AND WILL MARK BRAINLIEST!!! NEED ANSWERS TO ALL
Answer:
B and D have a horizontal line of symmetry ( their top and bottom parts match ) Some letters like X, H, and O, have vertical and horizontal lines of symmetry. some like P, R, and N have no lines of symmetry.
Step-by-step explanation:
A,. C,. D,. E,. H,. I,. M,. O,. T,. U,. V,. W,. X,. and Y have lines of reflective symmetry. Some of them have more than one.
'O' has an infinity of them.
There is no way for you to give extra points.
f(x) = 4(4 + x) whats the answer? and would that be the constant rate?
Answer:
f(x)=16+ 4x
the constant rate would be 4
Step-by-step explanation:
Answer: y=4x+16
Step-by-step explanation:
Mallory ordered a pizza with a 17-inch diameter. ricky ordered a pizza with a 20-inch diameter. what is the approximate difference in the area of the two pizzas?
Answer:
Ok so, pizza one is 17 inches in diameter, which in order to find area of a circle/circumferences, you first need to divide by 2, in this case 17/2=8.5, then square it, 8.5*8.5=72.25, then multiply by PI (3.14 in this case.) 72.25*3.14=226.865 which can round up to 227. Or 226.9
Step-by-step explanation:
Divide by 2
Square
Multiply by pi. (3.14)
Which triangle congurence theorem proves that ABD ≈ CBD?
AAS
SAS
HL
CPCTC
Answer:
AAS
Step-by-step explanation:
the ansewer
