1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
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
You might be interested in
Identify the lateral area and surface area of a regular triangular pyramid with base edge length 14 cm and slant height 15 cm.
sattari [20]
How did you get 315.
6 0
3 years ago
What is £42 increased by 10%
lara [203]
42+42 \cdot 10\%=42+42 \cdot 0.1=\underline{\underline{\pounds 46.2}}
3 0
3 years ago
Read 2 more answers
15 - 4x = 6 - 3x<br><br>whats the answer. ​
Makovka662 [10]

Answer:9

Step-by-step explanation: First you add the 3x to both sides(the -4x and the -3x) and then you get 15-1x=6. Next you subtract 15 from 15 and 6, so you get -1x=-9. So then you divide both sides by -1 (do -1x over -1 equals -9 over -1). Last you do the dividing and you get x=9.

5 0
3 years ago
Consider the original complex figure and the reduction.
Roman55 [17]

Answer: The answer is C. 5

Step-by-step explanation:

Just took the test on edg.

4 0
3 years ago
Hey guys help me with this question plzzzzzz​
Ad libitum [116K]

Answer:

625 cm³ and 64000 cm³

Step-by-step explanation:

Given

x = \sqrt[3]{V} ( cube both sides )

x³ = V

(a)

x = 25 cm , then

V = 25³ = 625 cm³

(b)

x = 40 cm , then

V = 40³ = 64 000 cm³

5 0
3 years ago
Other questions:
  • Please help me please
    10·1 answer
  • Pleaseeeeeee helpppp!!!!
    14·1 answer
  • The moon forms a right triangle with the earth and the sun during one of its phases I show a scientist measures the angle acts a
    10·1 answer
  • Divide. −5 1/3 ÷ 2 3/4
    5·2 answers
  • What is the percent of decrease of 90 to 72
    5·2 answers
  • I am having trouble with my homeschool homework. please help.
    9·1 answer
  • Please assist me in the geometry please !!!!
    8·1 answer
  • Help me please!!!!!!!!!!!!!!!!!!!
    9·2 answers
  • (6 x 10^2)\(3x10^-5)
    10·2 answers
  • Find the length of side xx to the nearest tenth.<br> 30°<br> 60°<br> x<br> 9
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!