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DanielleElmas [232]
3 years ago
9

I need to find the perimeter and area of the regular polygon.

Mathematics
1 answer:
mezya [45]3 years ago
7 0
The area of a polygon is given by the formula Area = ap/2 where a is the length of the apothem and p is the perimeter. The apothem is a line from the center of the polygon perpendicular to a side.

Depending on the formula you know, you can find the length of a side in 1 of 2 ways. 

The first way uses a triangle. Using the radius of the polygon you can create 8 congruent triangles. The center angle will be 360 / 8 = 45 and two side lengths of 20. You can find the length of the base using the law of cosines.

c^2 = 20^2 + 20^2 - 2(20)(20)(cos 45)
c^2 = 400 + 400 - 800(cos 45)
c^2 = 800 - 800(cos 45)
c = sqrt(800 - 800(cos 45)
c = 15.31

The second way is to use this formula:
r = s / (2 sin(180 / n))
20 = s / (2 sin(180/8)
(20)(2)sin(22.5) = s
(40)sin(22.5) = s
s = 15.31

We need to calculate the perimeter. As there are 8 sides (8)(15.31) = 122.48
Now we need to calculate the apothem using

a = S / (2 tan (180 / n)
a = 15.31 / (2 tan (180 / 8))
a = 18.48

Now solve for the area

Area = ap/2
Area = (18.48)(122.48)/2
Area = 1131.72

perimeter = 122.48
area = 1131.72
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Which is greater 192 inches or 5yards and 1 foot
makvit [3.9K]
1 yard = 36 inches. We have 5 yards, so 5x36 = 180

1 foot = 12 inches.

So the base 192 is largest.
3 0
3 years ago
A tree casts shadow 26 ft long. A 3 ft tall flowers casts a shadow 4 ft long. How tall is the tree?
Rufina [12.5K]

Answer:

19. 5 feets

Step-by-step explanation:

Shadow of tree = 26 feets

Height of flower = 3 feets

Shadow of flower = 4 feets

Height of sun Innthe sky:

Shadow of flower / height of flower

= 4/3 = 1.333333

Height of tree:

Shadow of tree / height of sun

26 feets / 1.33333

= 19.5 feets

Hence, height of tree = 19.5 feets

5 0
3 years ago
77
Bond [772]
\frac{77}{16} =  \frac{64+13}{16} = \frac{64}{16} + \frac{13}{16} =4 \frac{13}{16}=4.8125\\=4.81 \times 100~percent=481~percent\to\boxed {D}
5 0
3 years ago
Find the Measure of angle O<br> (see image)<br> Only real answers, please
-Dominant- [34]

Answer:

From the given figure we can see that :---

MN||PO, MN=PO and MP=NO

Therefore, angle M=angle N (adjacent sides of the trapezoid)

(8x - 16)  =  (6x + 20) \\ 2x = 36 \\  \boxed{x = 18}

angle M=angle N= (6×18)+20=108+20 =128°

angle O =(180°-128°)=52°

<h3>Hence, angle O is <u>52°.</u></h3>
3 0
2 years ago
A publisher reports that 45% of their readers own a laptop. A marketing executive wants to test the claim that the percentage is
nexus9112 [7]

Answer:

z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933  

p_v =2*P(z  

Step-by-step explanation:

Information given

n=370 represent the sample selected

\hat p=0.4 estimated proportion of  readers owned a laptop

p_o=0.45 is the value that we want to test

z would represent the statistic

p_v represent the p value

Creating the hypothesis

We need to conduct a hypothesis in order to test if the true proportion of readers owned a laptop is different from 0.45, the system of hypothesis are:  

Null hypothesis:p=0.45  

Alternative hypothesis:p \neq 0.45  

The statistic is:

z=\frac{\hat p -p_o}{\sqrt{\frac{p_o (1-p_o)}{n}}} (1)  

Replacing we got:

z=\frac{0.40 -0.45}{\sqrt{\frac{0.45(1-0.45)}{370}}}=-1.933  

Calculating the p value  

We have a bilateral test so then the p value would be:

p_v =2*P(z  

8 0
2 years ago
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