What is the surface area of the square pyramid?



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in²

Square pyramid net consisting of a square and four triangles. The square has length and width of eight inches. A triangle has a base of eight inches and a height of eleven inches.

Answers

Answer 1

Answer:

  240 in²

Step-by-step explanation:

The surface area of the pyramid is the sum of the areas of the parts of the composite figure comprising the net. That is, it is the sum of the areas of four triangles and a square.

__

Face

The area of a triangle is ...

  A = 1/2bh

For the given triangles, this is ...

  A = 1/2(8 in)(11 in) = 44 in²

__

Base

The area of the square base is ...

  A = s²

For the given dimensions, this is ...

  A = (8 in)² = 64 in²

__

Total Surface Area

The sum of the areas of the four faces and the base is ...

  total area = 4(44 in²) +64 in² = 240 in²

The surface area of the square pyramid is 240 in².


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Step-by-step explanation:

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Step-by-step explanation:

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Let x, y, and z denote the side lengths of the box, with the bottom face having dimensions x-by-y and z is the height. Naturally this means each of x, y, and z must be greater than 0.

The box has a fixed volume of 252 cm³, so

xyz = 252

The surface area of the box is

2xy + 2xz + 2yz

and we're told that the material cost for each face is different. The total cost of the material needed to make the box is given by

C (x, y, z) = ($5/cm²) xy + ($2/cm²) xy + 2 ($3/cm²) (xz + yz)

or, omitting units and simplifying,

C (x, y, z) = 7xy + 6 (x + y) z

In the volume constraint, solve for any one variable; I'll do z.

z = 252/(xy)

Substitute this into the cost function:

C (x, y, 252/(xy)) = 7xy + 1512 (x + y)/(xy)

Since this is now a function of 2 variables, I'll rewrite this as

C* (x, y) = 7xy + 1512 (1/y + 1/x)

Compute the partial derivatives of C and find the critical points:

∂C/∂x = 7y - 1512/x² = 0   ⇒   x² y = 216

∂C/∂y = 7x - 1512/y² = 0   ⇒   x y² = 216

It follows that

x² y = x y²   ⇒   x = y

Just like before, we can think about C* as yet another function but only of 1 variable,

C** (x) = 7x² + 3024/x

Now find the critical points of C** :

dC**/dx = 14x - 3024/x² = 0   ⇒   x = 6

All of this tells us that C (x, y, z) has a critical point when x = y = 6 and z = 252/6² = 7. So the box that costs the least has dimensions 6 × 6 × 7 cm, which gives the box a surface area of 240 cm² and a total cost of $756.

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Answers

Answer:

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Step-by-step explanation:

Hey there!

A triangle has to have three vertices that add up to 180 degrees

The angle measurments 50 and 40 are already given and added up, they equal 90 degrees

Now out of 180 degrees, 90 degrees is already shown

What you need to do now is try to find how much more degrees you need to get 180 degrees

As you know 180-90=90

So this means that the missing angle is 90 degrees

Now that we know this, we can find out what type of triangle this is

Since the triangle has an angle that is equal to 90 degrees, or it has a right angle, the triangle can be called a right triangle

A right triangle is a triangle that has an angle that is equal to 90 degrees

So this triangle is a right triangle

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Answer:

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Step-by-step explanation:

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Answers

Answer:

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Answers

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Step-by-step explanation:


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Answers

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Answer:

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Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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Step-by-step explanation:

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Answers

Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Step-by-step explanation:

Answer:

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Step-by-step explanation:

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Answers

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Step-by-step explanation:

Answer:

Step-by-step explanation:

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Step-by-step explanation:

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Answers

Answer:

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Step-by-step explanation:

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Answers

Step-by-step explanation:

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Answers

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Step-by-step explanation:

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Answers

Response

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Answers

Answer:

Step-by-step explanation:

Answer: 5.5

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Mark me brainliest as well please.

Answer:

i know i said it in the text but it's 5.5

Step-by-step explanation:

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