What is the lateral surface area of the square pyramid represented by this net?
Answers
Answer:
340 ft²
Step-by-step explanation:
From the diagram, we can see that the shape is made up of a square and 4 triangles. (We know it's a square as its width equals its length).
First, find the area of the square.
Area of a square = width x length = 10 x 10 = 100 ft²
All the triangles are the same, so we need to find the area of one of the triangles and multiply it by 4.
Area of a triangle = 1/2 x base x height = 1/2 x 10 x 12 = 60 ft²
So the total area of all 4 triangles = 4 x 60 = 240 ft²
Therefore the total surface area = 100 + 240 = 340 ft²
Answer:
340 ft²
Step-by-step explanation:
The surface area of a shape is basically the area of its faces.
[tex]\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}[/tex]
1. First, Let's find the area of the triangles. To find the area of a triangle, we need to multiply the height and the base and then divide the product by 2.
[tex]\rightarrow \text{Area of triangle} = \dfrac{12 \times 10}{2}[/tex]
Now, let's find the area of the triangle by simplifying the RHS.
[tex]\rightarrow \text{Area of triangle} = 6 \times 10[/tex]
[tex]\rightarrow \text{Area of triangle} = 60 \ \text{ft}^{2}[/tex]
Since there are four triangles, we need to further multiply the area of the triangle by 4 to find the area of four triangles.
[tex]\rightarrow \text{Area of four triangles} = 4(60)[/tex]
[tex]\rightarrow \text{Area of four triangles} = 240 \ \text{ft}^{2}[/tex]
2. Now, let's find the area of the square. To find the area of the square, we need to square the side length.
[tex]\rightarrow \text{Side length} = 10 \ \text{ft}[/tex]
[tex]\rightarrow \text{Area of square} = 10^{2}[/tex]
[tex]\rightarrow \text{Area of square} = 100 \ \text{ft}^{2}[/tex]
3. Lastly, let's find the surface area. To find the surface area of the figure, we need to sum up the area of the triangles and the area of the square.
[tex]\rightarrow \text{Surface area of pyramid: 4(Area of triangle) + Area of square}[/tex]
[tex]\rightarrow \text{Surface area of pyramid: 240 + 100}[/tex]
[tex]\rightarrow \text{Surface area of pyramid: 340 \text{ft}}^{2} }[/tex]
Related Questions
What is the period of the parent cosine function, y = cos(x)? degrees What is the period of the cosine function shown in the graph? degrees.
Answers
Answer:
1080°
Step-by-step explanation:
hope this helped <3
Answer: A,C,E
Step-by-step explanation:
edge 2023
Which graph represents y= square root x-4
Answers
Answer:
Find the domain by finding where the equation is defined. The range is the set of values that correspond with the domain.Domain: [4,∞),{x|x≥4}[4,∞),{x|x≥4}Range: [0,∞),{y|y≥0}
A speck of dust is 2.8 x 10-8 m wide. Which of the following is the best way
to rewrite this quantity, using more appropriate units?
О
A. 2.8 x 10-5 mm
B. 2.8 x 10-11 km
O C. 2.8 x 10-8 m
O D. 2.8 x 10-6 cm
Answers
Answer:
A.
Step-by-step explanation:
2.8 x 10 -5mm
Please Help writing equations!
Answers
Caleb drives 8 hours at 75 miles per hour. How far does he travel
Answers
Answer:
600 miles
Step-by-step explanation:
8*75=600
since he goes at 75 miles per hour and he drove 8 hours long, you multiply getting you 600 miles.
Calcula las dimensiones de un rectángulo que la base mide 6 centímetros más que su altura y tiene un área de 91 centímetros cuadrados.
Answers
La base y la altura del rectángulo mide 7 y 13 centímetros, respectivamente.
Cómo hallar las dimensiones de un rectángulo
Por geometría sabemos que el área de un rectángulo ([tex]A[/tex]), en centímetros cuadrados, es igual al producto de la base ([tex]b[/tex]) y la altura ([tex]h[/tex]), ambas en centímetros.
Mediante álgebra tenemos la siguiente expresión:
[tex]x\cdot (x+ 6) = 91[/tex]
[tex]x^{2}+6\cdot x - 91 = 0[/tex] (1)
Las raíces de este polinomio se determinan mediante la fórmula cuadrática:
[tex]x_{1} = 7[/tex], [tex]x_{2} = 13[/tex]
En consecuencia, la base y la altura del rectángulo mide 7 y 13 centímetros, respectivamente. [tex]\blacksquare[/tex]
Para aprender más sobre rectángulos, invitamos cordialmente a ver esta pregunta verificada: https://brainly.com/question/17048958
If there are 48 boys and 60 girls in a room, fll out all of the possible ratios of boys to girls that could be made.
I need 3 more ratios, please help me.
Answers
Answer:
Brainliest me pls
just keep scrolling you'll see my answer:)
[tex]\red{ \rule{0pt}{100000pt}} \orange{ \rule{0pt}{100000pt}} \color{yellow}{ \rule{0pt} {100000pt}} \green{ \rule{0pt} {100000pt}} \blue{ \rule{0pt} {100000pt}} \purple{ \rule{0pt} {100000pt}}[/tex]
Find the value of x. Round your answer to the nearest tenth.
Answers
Answer:
24.2 =x
Step-by-step explanation:
Since this is a right triangle, we can use a trig functions
cos theta = adj side / hypotenuse
cos 41 = x/ 32
32 cos 41 = x
24.1507=x
Round to the nearest tenth
24.2 =x
I gotta help my younger brother and k just don’t feel like using my brain at all
Answers
Answer:
use your phone calculator xD
Step-by-step explanation:
What is the volume of the prism above ? ?
Answers
Answer:
24
Step-by-step explanation:
In order to find the volume of something you would have to multiply the width x the length x the height which is 3x2x4 which equals to 24.
Answer:
24
Step-by-step explanation:
V=Bh
V=base area x length
3x2x4=24
24
what is the absolute and percentage difference between the two equations
Answers
3.4 cm
1.1 cm
2 cm
Find the area of each trapezoid
Answers
Answer:
What is the base and height????
n = 3m -11
2m + 3n = 0
Show how to find system of equations
Answers
Answer:
tranform the 1st one to: 3m-n=11
add the 1st and 2ns equations: 5m+2n=11
What is the solution to this inequality?
-9x - 15 < 3
O x < 2.
OX > 2
O x < -2 .
OX > -2
Answers
Answer:
x > - 2
Step-by-step explanation:
- 9x - 15 < 3 ( add 15 to both sides )
- 9x < 18
Divide both sides by - 9, reversing the symbol as a result of dividing by a negative quantity.
x > - 2
The solution to the inequality - 9x - 15 < 3 is, x > - 2.
What are inequalities and their types?Inequality is a relation that compares two numbers or other mathematical expressions in an unequal way.
The symbol a < b indicates that a is smaller than b.
When a > b is used, it indicates that a is bigger than b.
a is less than or equal to b when a notation like a ≤ b.
a is bigger or equal value of an is indicated by the notation a ≥ b.
Given, An inequality of the form - 9x - 15 < 3.
- 9x < 3 + 15.
- 9x < 18.
Now, Moving the variable to the other side to make it positive we have,
9x > - 18.
x > - 18/9.
x > - 2.
learn more about inequalities here :
https://brainly.com/question/30231190
#SPJ7
Write the slope-intercept form of the equation of each line
Answers
Answer:
slope intercept form- y=mx+b
m=slope
b=y-intercept
how to find slope= rise/run
how to fine y-intercept= go straight down the y axis (up and down in the center of the graph) until you come across a point
slope=3
y-intercept=-1
answer= 3x-1
The slope of line p is and the slope of line q is
Answers
Answer:
The slope of line p is 3, and the slope of line q is -3.
Step-by-step explanation:
PLEASEEE HELPPP!!! 55 POINTSSS!!
Answers
Answer:
min: -10
max: 18
minmax
Step-by-step explanation:
What is the solution of sqrtx + 2 - 15 = -3?
Answers
Please help
FIND THE VALUE OF X
Answers
hope that helped
I think they wrote the wrong answers but if y’all find out which one it is thanks
Answers
Answer:
8x^2+16x+16
Step-by-step explanation:
The combined area is the sum of both expressions.
2x^2-13x+21+6x^2+29x-5
8x^2+16x+16
8(x^2+2x+2)
You're right. The multiple choice is just wrong.
If 24 is increased to 30, the percent of increase is how much
%.
Answers
Answer:
25%
Step-by-step explanation:
[tex]percentage \: increase = \frac{30 - 24}{24} \times 100 \\ \\ = \frac{6}{24} \times 100 \\ \\ = \frac{1}{4} \times 100 \\ \\ = 25\%[/tex]
What is the initial value of the function represented by this graph
A. 0
B. 1
C. 2
D. 5
Answers
Answer:
2 because the initial value is y-intercept
It appears that the derivatives of sine and cosine are related. What about the second derivatives?.
Answers
Answer:
Step-by-step explanation:
[tex]\frac{d}{dx} (sin~x)=cos~x\\\frac{d}{dx}(cos~x) =-sin~x\\\frac{d^2}{dx^2} (sin~x)=\frac{d}{dx} (cos~x)=- sin~x\\\frac{d^2}{dx^2} (cos~x)=\frac{d}{dx} (-sin~x)=-cos~x[/tex]
For the graph of the function, Identify the axis of symmetry, vertex and the formula for the function.
Answers
Each of 5 boys randomly chooses a watch from 12 different styles. What is the probability that at least 2 boys choose the same type of watch?
Answer with explanation gets brainliest.
Answers
Answer:
Ok. So we have 12 different styles of watches to choose from, so that means that the total number of combinations of styles for 5 boys is 12*12*12*12*12, since each boy has his pick of 12 options.
The way to answer this question is by way of the complementary rule: We want the number of ways that the boys can all have different styles. So the first boy to pick has 12 options available to him, the second boy has 11 options available to him, the 3rd boy has 10 options available to him, so on and so forth.
So the probability that the boys all have different watches is (12*11*10*9*8)/12^5= .3819.
To find the probability that at least two boys have the same style would just be 1 -.3819 = 6181
What is the best approximation of the value of a? 2. 4 cm 2. 7 cm 3. 0 cm 3. 3 cm.
Answers
You can use the sine law for the given triangle to find the measure of a.
The value of a is given by
Option D: 3 cm
What is law of sines?For any triangle ABC, with side lengths |AB| = c units, |BC| = a units, and |AC| = b units, then
[tex]\dfrac{sinA}{a} = \dfrac{sinB}{b} = \dfrac{sinC}{c}[/tex]
(If you draw it, you will notice that sin of an angle is sitting over the side length of its opposite side. This is the most important thing that people can mistake most commonly).
Using the above fact to calculate the measure of 'a' for the given contextWe have these data
sin A = sin(40 degrees) = 0.643 approx
sin(b) = sin(95) degrees) = 0.996 approx
b = 4.7 cm
Using the first two inequalities, we get
[tex]\dfrac{sinA}{a} = \dfrac{sinB}{b} \\\\\dfrac{0.643}{a} = \dfrac{0.996}{4.7}\\\\a = \dfrac{0.643}{0.212} \approx 3 \: \rm cm[/tex]
Thus,
The value of a is given by
Option D: 3 cm
Learn more about sine law here:
https://brainly.com/question/17289163
Answer:D
Step-by-step explanation:
The trip from Carville to Nikpath requires $4\frac 12$ hours when traveling at an average speed of 70 miles per hour. How many hours does the trip require when traveling at an average speed of 60 miles per hour? Express your answer as a decimal to the nearest hundredth.
Answers
From the given speed and time, the distance of the trip can
be determined.
Correct response;
Number of hours the trip will take when traveling 60 mph is [tex]\underline{5\frac{1}{4} \ hours}[/tex] How is the time taken at a given speed calculated?Given;
Time required for the trip from Carville to Nikpath = [tex]4\frac{1}{2}[/tex] hours
Average speed for the trip = 70 mph
Required;
The duration of the trip when traveling 60 mph
Solution;
Distance = Velocity × Time
Distance of trip = [tex]\mathbf{4\frac{1}{2}}[/tex] hour × 70 miles/hour = 315 miles
Duration of trip when traveling 60 mph is therefore;
[tex]Time = \dfrac{315 \, miles}{60 \ miles/hour} = 5.25 \ hours = \mathbf{ 5\frac{1}{4} \ hours}[/tex]
Duration of trip when traveling 60 mph = [tex]\underline{5\frac{1}{2} \ hours}[/tex]
Learn more about speed and time calculations here;
https://brainly.com/question/10113134
The average of two numbers is 55. Ir their positive difference is 64, then determine the two numbers algebraically.
Answers
Answer:23,87
Step-by-step explanation:
call the 2 numbers x and y
average of 2 numbers being 55 means (x+y)/2 = 55
if the positive difference of the two numbers is 64 then x-y=64
since you have two equations and two variables you can solve for x and y
(x+y)/2 = 55 --> x+y=110
x-y=64 --> x=64+y
x+y=110 and x=64+y --> 64+y+y=110
y=23
x=87
the two numbers are 23 and 87
Answer:
87,23
Step-by-step explanation:
Let larger number be x other smaller number be y,
Given,
(x+y)/2=55
or, x+y=110---(i)
x-y=64---(ii)
Adding eqn (i) & (ii), we get,
x+y=110
+x-y=64
2x=174
x=87
Again,
Putting x=87 in eqn (ii), we get,
87-y=64
87-64=y
y=23
Heather spent a total of 70 minutes working out at the gym.
She spent 20 minutes longer running on the treadmill than she spent lifting weights.
When t represents the time Heather spent running on the treadmill and w represents the time she spent
lifting weights, which system of equations represents this situation?
t-w= 20
o
t=w - 70
t + w= 70
O
w=t+ 20
t-w= 20
O
w= t - 70
t + w= 70
t = W + 20
Answers
Answer:
choice 4
Step-by-step explanation:
t = treadmill time
w = wt lift time
70 is total time
so t+w = 70
next t is 20 more than w
t = w+20
Answer:
choice four, took the test and got it right
Step-by-step explanation:
Find the value of x. If necessary, write your answer in simplest radical form.
(Simplify your answer. Type an exact answer, using radicals as needed.)
Answers
Answer:
[tex]x=\sqrt{6}[/tex]
Step-by-step explanation:
To find the hypotenuse, it is [tex]a^{2}+b^{2}=c^{2}[/tex]
So...
[tex]1^{2}+x^{2} =\sqrt{7}\\1+x^{2} =\sqrt{7} \\x=\sqrt{6}[/tex]
