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
serious [3.7K]
3 years ago
12

Please help i put a picture below

Mathematics
1 answer:
PSYCHO15rus [73]3 years ago
5 0

Answer:

Step-by-step explanation:

This is not nearly as threatening and scary as I first thought it was.  You must be in the section in Geometry where you are taught that perimeter of similar figures exist in a one-to-one relationship while areas of similar figures exist in a squared-to-squared relationship.  We will use that here.  

The area formula for a regular polygon is

A=\frac{1}{2}ap where a is the apothem and p is the perimeter.  We are first asked for the area of the polygon, but it would make more sense to find the perimeter first, since we need it to find the area.

P = 5(8) so

P = 40

We are given that the area of the triangle inside that polygon is 22.022 units squared.  Knowing that the area formula for a triangle is

A=\frac{1}{2}bh we can sub in what we know and solve to find the height:

22.022=\frac{1}{2}(8)h and

22.022 = 4h so

h = 5.5055 units

It just so happens that the height of that triangle is also the apothem of the polygon, so now we have what we need to find the area of the polygon:

A=\frac{1}{2}(5.5055)(40)

which gives us an area of

A = 110.11 units squared.

Here is where we can use what we know about similar figures and the relationships between perimeters and areas.  We will set up a proportion with the smaller polygon info on top and the larger info on bottom.  We know that the larger is 3 times the smaller, so the ratio of smaller to larger is

\frac{s}{l}:\frac{1}{3}

Since perimeter is one-to-one and we know the perimeter of the smaller, we can create a proportion to solve for the perimeter of the larger:

\frac{s}{l}:\frac{1}{3}=\frac{40}{x}

Cross multiply to get that the perimeter is 120 units.  You could also have done this by knowing that if the larger is 3 times the size of the smaller, then the side measure of the larger is 24, and 24 * 5 = 120.  But we used the way we used because now we have a means to find the area of the larger since we know the area of the smaller.

Area exists in a squared-to-squared relationship of the perimeter which is one-to-one.  If the perimeter ratio is 1:3, then the area relationship is

\frac{s}{l}:\frac{1^2}{3^2} which is, simplified:

\frac{s}{l}:\frac{1}{9}

Since we know the area for the smaller, we can sub it into a proportion and cross multiply to solve for the area of the larger.

\frac{s}{l} :\frac{1}{9} =\frac{110.11}{x}

A of the larger is 990.99 units squared

You might be interested in
N is an integer greater than 1.
Whitepunk [10]
I dont understand the question

7 0
3 years ago
Evaluate 7j+5-8k when j=0.5 and k=0.25
dlinn [17]

So first you would substitute j and k in the expression.

7(0.5)+5-8(0.25)

3.5+5-2

It would equal 6.5

Hope this helps!

6 0
3 years ago
Read 2 more answers
Dora is building the right square pyramid shown in the diagram.
saul85 [17]
Answer is 4 :) I hope it help you.
8 0
3 years ago
Given triangle DEF where ∠D = (7b +1)∘, ∠E = (2b + 1)∘, and ∠F = ( b + 8)∘. What is the measure of ∠E?
____ [38]
<h3>Answer:  35 (choice C)</h3>

=============================================

Explanation:

For any triangle, the three interior angles always add to 180.

D+E+F = 180

(7b+1) + (2b+1) + (b+8) = 180

(7b+2b+b) + (1+1+8) = 180

10b+10 = 180

10b = 180-10

10b = 170

b = 170/10

b = 17

Use this value of b to find the three angle measures

  • D = 7b+1 = 7*17+1 = 119+1 = 120
  • E = 2b+1 = 2*17+1 = 34+1 = 35 degrees
  • F = b+8 = 17+8 = 25

As a check,

D+E+F = 120+35+25 = 120+60 = 180

which helps confirm the correct answers.

3 0
3 years ago
What is the MINIMUM of the data set: 35, 20, 30,25, 20?"
Romashka [77]

Answer:

B) 20

<u>The minimum of a data set is the </u><u>smallest</u><u> term of that set.</u>

We arrange the terms in ascending order

→ 20,20,25,30,35

So, the minimum is 20

<u>--------------------------------</u>

<u>hope it helps...</u>

<u>have a great day!!</u>

3 0
3 years ago
Other questions:
  • The price for digital downloads of music is represented by the linear functions f(x) shown on the graph. The price for digital d
    8·1 answer
  • mack plans to meet his 4 friends. how many different ways can he make his visit if he visits each friend once?
    10·1 answer
  • What is the product of any integer and –1?
    10·1 answer
  • Explain how you plotted the points in part a
    8·2 answers
  • What factors do 28 and 44 have in common?
    15·1 answer
  • Angle BDC measures 42°. What is the measure of angle BAC
    12·1 answer
  • Is it possible to draw an isosceles right triangle with side lengths 5,5,and 10? Explain.
    13·1 answer
  • Find the value of x and each arc measure
    9·1 answer
  • The Chapin Social Insight Test evaluates how accurately the subject appraises other people socially. In the reference population
    9·1 answer
  • Write an expression for 12 times a number c.
    9·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!