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Evgesh-ka [11]
3 years ago
12

A triangular pyramid has a base shaped like an equilateral triangle. The legs of the equilateral triangle are all 20 inches long

, and the height of the equilateral triangle is 17.3 inches. The pyramid's slant height is 13 inches. What is its surface area?
Mathematics
1 answer:
Pie3 years ago
6 0

Answer:

Surface area of pyramid with base equilateral triangle is 390+100\sqrt{3} square inches

Step-by-step explanation:

Recall the following result:

The total surface area(S) of a regular pyramid is given by,

S = \frac{1}{2}pl+B                                       ...... (1)

Here, p represents the perimeter of the base , l the slant height and B the base area of the pyramid.

From the given information:

Side of equilateral triangle = 20 inches

Slant height of the pyramid(l) = 13 inches.

First find the perimeter and Area of the base pyramid.

Perimeter of equilateral triangle(p) = 3 \times (side)

                                                          = 3 \times 20 = 60 inches

Area of equilateral triangle(B) = \frac{\sqrt{3} }{4} \times (side)^{2}

                                                 =\frac{\sqrt{3} }{4} \times (20)^2 = 100\sqrt{3}  square inches.

Substitute the above values in equation (1) as shown below:

S=\frac{1}{2} \times 60 \times 13+100\sqrt{3}

S= 390+100\sqrt{3} square inches

Hence, the surface area of pyramid with base equilateral triangle is 390+100\sqrt{3} square inches.

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The diagram shows a square pyramid over a cube. What is the volume of the entire figure?
TEA [102]

Answer: 810

Step-by-step explanation:

first lets take down the information we were given,

height (h) of the pyramid should be 12 - 9 = 3

base (a) = 9

So we calculate the volume of a square pyramid

V = a²h/3

V = (9² × 3) / 3

v = (81 × 3) / 3

V = 81

now we calculate the volume of the cube using the formula

V = a³

V = 9³

V = 729

NOW to get the volume of the entire figure

we say

volume of square pyramid + volume of cube

81 + 729 = 810

3 0
3 years ago
Below is the five-number summary for 136 hikers who recently completed the John Muir Trail (JMT). The variable is the amount of
Fudgin [204]

Answer:

Option B) There were less hikers between Q1 and the median than there were between the median and Q3

Step-by-step explanation:

The given five-number summary is:

Minimum     :     9

Q1                :     18  

Median        :     21  

Q3               :     28  

Maximum    :     56  

Now based on these numbers we will evaluate the given options:

Option A)

Most people finished the JMT within 9 to 56 days, but some took a little longer.

This statement is false because minimum time is 9 days and maximum time is 56 days. This means all of the people finished JMT within 9 to 56 days. As 56 is the maximum, no one took longer than this to finish JMT. Hence, this option is Wrong.

Option B)

There were less hikers between Q1 and the median than there were between the median and Q3

Difference between median and Q1 = 21 - 18 = 3

Difference between Q3 and median = 28 - 21 = 7

So, the given statement is true as there are 3 hikers between Q1 and the median and 7 hikers between the median and Q3. Thus this statement is Correct.

Option C)

Exactly 36 hikers had times ranging from 18 to 21 days

18 days is the Q1 and 21 days represent median. Remember that Q1 is the 25th percentile and Median is the 50th percentile. So 25% of the hikers will have time ranging from 18(25th percentile) to 21 days(50th percentile).

Since, total number of hikers is 136, and 25% of 136 is 34. This means, 34 hikers had times ranging from 18 to 21 days. Thus, this statement is Wrong.

Option D)

At least 36 hikers completed the JMT within 28 to 56 days.

28 days represent Q3, the 3rd quartile or 75th percentile and 56 days represent the maximum value. So there are 25% of the hikers will finish between 28 days and 56 days.

25% of 136 is 34. This means 34 hikers completed the JMT within 28 to 56 days. Therefore, this statement is also wrong.

Hence, option B gives the most accurate description about the given five-number summary.

6 0
4 years ago
I NEED HELP WITH THIS
Taya2010 [7]

Answer:

B.

Step-by-step explanation:

You must first subtract 12 from 27, which marks out two answers. A, and D.

Then, if NAthan traveled 3 times as far s philip, then you would multiply by three. leaving you with the only option being,

B.

7 0
3 years ago
Read 2 more answers
An envelope from the post office is 3 inches wide with a total area of 30 square inches.what is the height of the envelope
ad-work [718]
The height of the envelope is 10. This is because you divide the area by 3. So, the missing side is 10 inches.

7 0
3 years ago
Read 2 more answers
Find the distance between the points (-8, -3) and (-2, 5). Hint: Use the Pythagorean theorem. ​
Drupady [299]

Answer:

1/5

Step-by-step explanation:

Use Pythagoras theorem

5 0
2 years ago
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