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Ber [7]
3 years ago
11

Peter has built a gazebo, whose shape is a regular heptagon, with a side length of $1$ unit. He has also built a pathway around

the gazebo, of constant width $1$ unit, as shown below. (Every point on the ground that is within $1$ unit of the gazebo and outside the gazebo is covered by the pathway.) Find the area of the pathway.
Mathematics
1 answer:
Sholpan [36]3 years ago
5 0

Answer:

Area of pathway = 10.375 unit²

Step-by-step explanation:

Given - Peter has built a gazebo, whose shape is a regular heptagon, with

             a side length of 1 unit. He has also built a pathway around the

             gazebo, of constant width 1 unit, as shown below.

To find -  Find the area of the pathway.

Proof -

Central angle = \frac{360}{7} = 51.43°

Now,

Central angle / 2 = \frac{360}{14} = 25.71°

And

height = \frac{1}{2}.\frac{1}{tan25.41} = 1.038

Now,

Inner area of gazebo = 7·\frac{1}{2}·1·(1.038) = 3.634 unit²

Outer area of gazebo = (\frac{2.038}{1.038})²·(3.364) = 14.009 unit²

∴ we get

Area of pathway = Outer area - Inner area

                            = 14.009 - 3.634

                            = 10.375 unit²

⇒Area of pathway = 10.375 unit²

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2 years ago
Write 12 ten thousands, 8 thousands,14 hundreds, 7 ones in standard form
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<span><u><em>The correct answer is: </em></u>
129,407.

<u><em>Explanation</em></u><span><u><em>: </em></u>
12 ten-thousands = 12*10000=120,000.
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<u>this gives us</u> 120,000+8,000=128,000.

14 hundreds = 14*100=1400;
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Read 2 more answers
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The question is incomplete. The map is attached as a photo and here is the complete question:

a. What is the actual distance between Saugerties and

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b. Catskill is 15 miles from Saugerties. What would the

distance on the map be? ___________________________

c. On another map, the distance between Saugerties and

Kingston is 2 inches. What would the distance from Saugerties to

Catskill be on this map? __________________

Since you have asked the answer for part (c) only, here is the answer:

Answer:

<u>The distance from Saugerties to Catskill would be </u><u>3 inches</u><u> on this map.</u>

Step-by-step explanation:

On the given map, the distance between Saugerties and Kingston is 4 inches and the scale is <u>1 inch = 2.5 miles.</u>

To calculate the actual distance in miles between Saugerties and Kingston, consider the given scale:

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Cross multiplying:

1x = 2.5 x 4

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The scale on the other map is 1 inch = 5 miles.

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Cross multiplying:

15 = 5y

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The distance from Saugerties to Catskill would be 3 inches on this map.

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