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Vilka [71]
3 years ago
5

What is the area of a regular hexagon (6 sides) whose

Mathematics
1 answer:
Ganezh [65]3 years ago
8 0

Step-by-step explanation:

With reference to the regular hexagon, from the image above we can see that it is formed by six triangles whose sides are two circle's radii and the hexagon's side. The angle of each of these triangles' vertex that is in the circle center is equal to 360∘6=60∘ and so must be the two other angles formed with the triangle's base to each one of the radii: so these triangles are equilateral.

The apothem divides equally each one of the equilateral triangles in two right triangles whose sides are circle's radius, apothem and half of the hexagon's side. Since the apothem forms a right angle with the hexagon's side and since the hexagon's side forms 60∘ with a circle's radius with an endpoint in common with the hexagon's side, we can determine the side in this fashion:

tan60∘=opposed cathetusadjacent cathetus => √3=Apothemside2 => side=(2√3)Apothem

As already mentioned the area of the regular hexagon is formed by the area of 6 equilateral triangles (for each of these triangle's the base is a hexagon's side and the apothem functions as height) or:

Shexagon=6⋅S△=6(base)(height)2=3(2√3)Apothem⋅Apothem=(6√3)(Apothem)2

=> Shexagon=6×62√3=216

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A pole that is 2.5 m tall casts a shadow that is 1.47 m long. At the same time, a nearby tower casts a shadow that is 36.25 m lo
Roman55 [17]

The tower is 61.65 meters tall.

<u>SOLUTION: </u>

Given that, a pole that is 2.5 m tall casts a shadow that is 1.47 m long.  

At the same time, a nearby tower casts a shadow that is 36.25 m long.  

We have to find height of the tower.  

Now, we know that,

2.5 \mathrm{m} \text { tall } \rightarrow 1.47 \text { long shadow }

Then, (let it be) n meter tall \rightarrow 36.25 long shadow

So, by cross multiplication method,

\Rightarrow \frac{2.5}{1.47}=\frac{n}{36.25}

This can be written as,

\Rightarrow 36.25 \times 2.5=1.47 \times n \rightarrow 1.47 n=90.625 \rightarrow n=61.649 \rightarrow n=61.65 \text{ m}

Cross multiplications steps: (To find Single Variable)

  1. Multiply the numerator of the left-hand fraction by the denominator of the right-hand fraction.
  2. Multiply the numerator of the right-hand fraction by the denominator of the left-hand fraction.
  3. Set the two products equal to each other.
  4. Solve for the variable.
6 0
3 years ago
Which term best completes the state all _______ are rectangles A. Parallelograms B.squares C.rhombi D. None of theses
liq [111]

Answer:

The answer is B. squares.

Step-by-step explanation:

All squares are considered rectangles. Not all parallelograms are rectangles, and rhombi are not rectangles.


I hope this helped! :-)

8 0
3 years ago
The graph of y=f(x) is above. If f(−4)=k, what is the value of f(k)?
cupoosta [38]

Answer:

B

The answer is B, which is -1.5.

3 0
3 years ago
Solve for X:
galben [10]

Answer:

A. -61/9

Step-by-step explanation:

(7x + 28) + (7x +28) = 5x - 5 . . . . . . . given equation

14x +56 = 5x -5 . . . . . . . . . . . . . . . . . collect terms

9x = -61 . . . . . . . . . . . . . . . . . . . . . . . . subtract 5x+56

x = -61/9 . . . . . . . . . . . . . . . . . . . . . . . . divide by the coefficient of x

4 0
3 years ago
Read 2 more answers
Find the selling price of a $50 item after a 50 % markup
siniylev [52]

Answer:

75 dollars

Step-by-step explanation:

If an item is 50 and you want to markup 50%, you must find 50% of 50 to find how much the item will go up by from 50.

So 50% of 50 means 50% times 50.

50%=.5 or 1/2

So .5(50)=25.

The item is going up by 25 dollars.

So we started at 50 dollars.

So 50+25 is going to be the new amount.

50+25=75 is the new amount.

5 0
3 years ago
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