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
VARVARA [1.3K]
3 years ago
9

How do I find the area of the shaded region?

Mathematics
1 answer:
vovangra [49]3 years ago
4 0

Answer:

Part a) The area of the shaded region is A=25(\frac{2\pi}{3}-\sqrt{3})\ cm^2

Part b) The area of the shaded region is A=18(3\pi-2\sqrt{2})\ cm^2

Step-by-step explanation:

Part a) we know that

step 1

Find the area of the sector

we know that

The area of a circle subtends a central angle of 2π radians

so

using proportion

Find the area of the sector by a central angle of π/3 radians

\frac{\pi r^2}{2\pi}= \frac{x}{\pi/3} \\\\x=\frac{\pi r^2}{6}

we have

r=10\ cm

substitute

x=\frac{\pi (10)^2}{6}\\\\x=\frac{50\pi}{3}\ cm^2

step 2

Find the area of triangle

The area of triangle is equal to

A=\frac{1}{2} (10^2)sin(\frac{\pi}{3})

Remember that

\frac{\pi}{3}=60^o

so

A=50(\frac{\sqrt{3}}{2})=25\sqrt{3}\ cm^2

step 3

Find the area of the shaded region

The area of the shaded region is equal to the area of the sector minus the area of isosceles triangle

so

A=(\frac{50\pi}{3}-25\sqrt{3})\ cm^2

Simplify

A=25(\frac{2\pi}{3}-\sqrt{3})\ cm^2

Part b) we know that

step 1

Find the area of the sector

we know that

The area of a circle subtends a central angle of 360 degrees

so

using proportion

Find the area of the sector by a central angle of 135 degrees

\frac{\pi r^2}{360^o}= \frac{x}{135^o} \\\\x=0.375\pi r^2

we have

r=12\ cm

substitute

x=0.375\pi (12)^2\\\\x=54\pi\ cm^2

step 2

Find the area of triangle

The area of triangle is equal to

A=\frac{1}{2} (12^2)sin(135^o)

A=72(\frac{\sqrt{2}}{2})=36\sqrt{2}\ cm^2

step 3

Find the area of the shaded region

The area of the shaded region is equal to the area of the sector minus the area of isosceles triangle

so

A=(54\pi-36\sqrt{2})\ cm^2

Simplify

A=18(3\pi-2\sqrt{2})\ cm^2

You might be interested in
Determine the missing factor
kogti [31]

Answer:

2x-1

Step-by-step explanation:

Just solve this way.

(2/3)x-(1/3)=(1/3)y.

Now find y in terms of x.

8 0
2 years ago
Question 11 Multiple Choice Worth 1 points)
Ann [662]
I think it would be 35
5 0
2 years ago
Name two points on a line that has a slope of 5 over 8.
GREYUIT [131]
Y=mx+b ....formula of slope

m refers to slope and b is intercept,,,so this become equation of y.
now answer,
y=5/8x+b 
6 0
3 years ago
Three friends are riding bicycles in a race. Sergio is 1.8 mi ahead of John. Albert is 0.5 mi behind Sergio. If John has ridden
Ilia_Sergeevich [38]
Albert has ridden 1.3 mi
3 0
3 years ago
<img src="https://tex.z-dn.net/?f=%20%5Cfrac%7Bx%7D%7B10.1%7D%20%20%3D%203.5" id="TexFormula1" title=" \frac{x}{10.1} = 3.5" al
dsp73

Answer:

x=35.35

Step-by-step explanation:

If you multiply \frac{x}{10.1} .1 by 10.1 that will cancel out the 10.1s, then since you multiplies one side of the equation by something you have to multiply the other too.  So 3.5*10.1 = 35.35.  Then since the 10.1s canceled out this leaves us with x=35.35.  Let me know if you need any more help.  

5 0
3 years ago
Other questions:
  • Are the ratios 21/149 and 30/70 equivalent explain pls help
    11·2 answers
  • Choose 2 answers one for the center and one for the spread
    14·1 answer
  • How do I do #12? <br><br> Please show all work. <br><br> Please help!
    13·1 answer
  • Heeeeeeeelllllllllllllppppppppp plz i need this fast
    7·1 answer
  • PLEASE HELP ME!!!! i dont get this at all
    14·1 answer
  • The table shows ticket prices for the local minor league baseball team for fanclub members and non-members. For how many tickets
    14·2 answers
  • A kite JMKL has diagonals JK and LM that intersect at point N. Which of the following options best describe the kite? Select all
    12·2 answers
  • Which is true about the domain and range of each function? Both the domain and range change. Both the range and domain stay the
    8·2 answers
  • Add. Write your answer in simplest form.<br> 2 5/6 + 3 2/5
    10·2 answers
  • Eric has 12 trophies in his room 9 of them are for football what percentage of the total number of sports trophies are his footb
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!