PLEEASSSSEEEE HHEEEEELLLLPPPPPPPP !!!!!!!!!!!!!!!!!!!!!!!!!!! Circle R is shown. Line segments Q R and S R are radii. The length
of Q R is 18. Sector Q R S is shaded. The measure of central angle QRS is StartFraction 8 pi Over 9 EndFraction radians. What is the area of the shaded sector? 36Pi units squared 72Pi units squared 144Pi units squared 324Pi units squared
2 answers:
Answer:
Step-by-step explanation:
In the attached diagram, circle R is shown. Line segments QR and SR are radii and QR = SR = 18 units.
The measure of the central angle QRS is
1. Find the area of the whole circle:
2. Note that the whole circle is determined by the full rotation angle with measure radians. So,
So, write a proportion:
Cross multiply
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Answer:
slope =
Step-by-step explanation:
Calculate slope m using the slope formula
m =
with (x₁, y₁ ) = (0, - 2) and (x₂, y₂ ) = (4, 0) ← 2 points on the line
m = =
=
=
Since the given hexagon is a regular hexagon all it's sides will be of equal length. Now, we know that the Area of any regular hexagon is given by:
Where is the area of the regular hexagon
is the side length of the regular hexagon
Also, it's Perimeter is given by:
Thus, all that we need to do is to find the side length of any one of the sides and to do that let us have a look at at the data of vertices points given and find out which points are definitely adjacent to each other and are also easy to calculate.
A quick search will yield that D(8, 0) and E(4, 0) are definitely adjacent to each other.
Please check the attached file here for a better understanding of the diagram of the original regular hexagon. Points D and E indeed are adjacent to each other.
Let us now find the distance between the points D and E using the distance formula which is as:
Where is the distance.
and
are the coordinates of points D and E respectively. (please note that interchanging the values of the coordinates will not alter the distance
)
Applying the above formula we get:
We know that this distance is the side length of the given regular hexagon.
Now, if the sides of the given regular polygon are reduced by 40%, then the new length of the sides will be:
Thus, the area of the smaller hexagon will be:
unit squared
and the new smaller perimeter will be:
unit
Which are the required answers.
