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
wariber [46]
3 years ago
7

In the regular octagon, the numeric value of the area of the shaded region is twice more than the numeric value of the length of

AB. Find the area of the unshaded region.
Mathematics
1 answer:
s2008m [1.1K]3 years ago
8 0

Answer:

A =  (2+√8)L² - 2L, where L is the length of AB

Step-by-step explanation:

Lets call L the length of one side. The octagon can be divided in 8 triangles composed by the vertices of the octagon and the center. The base of each triangle has length L and the height is L/2 + M, with M such that 2M² = L². This is because the center of the octagon is located at middle height of the center sides. You can reach that height by 'travelling' from the bottom side throught one slanted side (which is the hypotenuse of a isosceles rectangle triangle of height M) and then you travel throught a center side half its length. Thus, h = L/2 + L/√2.

The area of each triangle of the octagon therefore is, as a result, h*L/2 = L²/4 + L²/2√2

Hence, the area of the octagon is 8*(L²/4 + L²/2√2) = (2+√8)L². The unshaded region area can be computed by taking this number and substract to it the value of 2L, which is the area of the shaded region (The double of the length of a side)

As a result,

A =  (2+√8)L² - 2L

You might be interested in
Find the value of x if A, B, and C are collinear points and B is between A and C.
Andrew [12]

Answer:

x = 6

Option A.

Step-by-step explanation:

We know that

If A, B and C are collineal points, they all pass through a common line.

<--------------14-------------->

A-----------B----------------C

<-----x-----><------x+2---->

Based on the problem and the diagram above,

(x) + (x+2) = 14

(2x+2) = 14

(2x) = 12

(x) = 6

7 0
3 years ago
Jane calculated the circumference of a circle to be 36π. what is the area if the circle
marshall27 [118]

Answer:

103.13

Step-by-step explanation:

A=πr2

C=2πr

A=C2

4π=362

4·π≈103.1324

4 0
2 years ago
On a necklace of 100 beads, 45 of the beads are round. The rest of the
mina [271]

Answer:

45% round 55% rectangular

8 0
2 years ago
Read 2 more answers
A bicyclist goes 43.54 miles in 3.5 hours. What is her speed?
Studentka2010 [4]
Divide 43.54 by 3.5
She was going 12.33 miles an hour
6 0
3 years ago
Read 2 more answers
A coin, having probability p of landing heads, is continually flipped until at least one head and one tail have been flipped. (a
Natali [406]

Answer:

(a)

The probability that you stop at the fifth flip would be

                                   p^4 (1-p)  + (1-p)^4 p

(b)

The expected numbers of flips needed would be

\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1}  = 1/p

Therefore, suppose that  p = 0.5, then the expected number of flips needed would be 1/0.5  = 2.

Step-by-step explanation:

(a)

Case 1

Imagine that you throw your coin and you get only heads, then you would stop when you get the first tail. So the probability that you stop at the fifth flip would be

p^4 (1-p)

Case 2

Imagine that you throw your coin and you get only tails, then you would stop when you get the first head. So the probability that you stop at the fifth flip would be

(1-p)^4p

Therefore the probability that you stop at the fifth flip would be

                                    p^4 (1-p)  + (1-p)^4 p

(b)

The expected numbers of flips needed would be

\sum\limits_{n=1}^{\infty} n p(1-p)^{n-1}  = 1/p

Therefore, suppose that  p = 0.5, then the expected number of flips needed would be 1/0.5  = 2.

7 0
2 years ago
Other questions:
  • Apples cost $0.95 per pound. How much would 1.6 pounds of apples cost
    10·2 answers
  • PLZZZZ HELP FAST!!!!
    5·2 answers
  • Solve for x:<br> 7x + 68°<br> 2x + 103°
    11·1 answer
  • Find the square root number of 36
    11·2 answers
  • Multiply 12x2y4z(-4x3y6z2)
    15·1 answer
  • 56,426+17,895
    7·2 answers
  • What is the LCM of 24 and 90?​
    8·2 answers
  • PLZ HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! :)
    11·1 answer
  • What is the density of 9 cm³ gold cube with 450 g in a mass?​
    13·1 answer
  • Can someone help me and solve the following equation showing work please? <br> thank you!
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!