What is the lateral surface area of the square pyramid represented by this net?

What Is The Lateral Surface Area Of The Square Pyramid Represented By This Net?

Answers

Answer 1

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 2

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]


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Step-by-step explanation:

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Answers

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Answers

You can use the sine law for the given triangle to find the measure of a.

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Option D: 3 cm

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Using the above fact to calculate the measure of 'a' for the given context

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[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]

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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

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Distance = Velocity × Time

Distance of trip = [tex]\mathbf{4\frac{1}{2}}[/tex] hour × 70 miles/hour = 315 miles

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[tex]Time = \dfrac{315 \, miles}{60 \ miles/hour} = 5.25 \ hours = \mathbf{ 5\frac{1}{4} \ hours}[/tex]

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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...

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