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
earnstyle [38]
3 years ago
9

each side of triangle xyz has length 9 .Find the area of the region inside the circumcircle of the triangle but outside the tria

ngle. PLEASE HELP QUICK!

Mathematics
1 answer:
mote1985 [20]3 years ago
6 0

Answer:

The area of the region inside the circumcircle of the triangle but outside the triangle is

A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find the area of triangle

we have an equilateral triangle

Applying the law of sines

A_t=\frac{1}{2}(b^2)sin(60^o)

where b is the length side of the equilateral triangle

we have

b=9\ units

A_t=\frac{1}{2}(81)sin(60^o)

A_t=\frac{1}{2}(81)\frac{\sqrt{3}}{2}

A_t=81\frac{\sqrt{3}}{4}\ units^2

step 2

Find the area of circle

The area of the circle is equal to

A_c=\pi r^{2}

The formula to calculate the radius of the circumcircle of the triangle equilateral is equal to

r=b\frac{\sqrt{3}}{6}

where b is the length side of the equilateral triangle

we have

b=9\ units

substitute

r=(9)\frac{\sqrt{3}}{6}

r=3\frac{\sqrt{3}}{2}\ units

Find the area

A_c=\pi (3\frac{\sqrt{3}}{2})^{2}

A_c=\frac{27}{4} \pi\ units^2

step 3

Find the area of the shaded region

we know that

The area of the region inside the circumcircle of the triangle but outside the triangle is equal to the area pf the circle minus the area of triangle

so

A=(\frac{27}{4} \pi-81\frac{\sqrt{3}}{4})\ units^2

Simplify

A=\frac{27}{4}[\pi-3\sqrt{3}]\ units^2

You might be interested in
To​ ​ get​ ​ an​ ​ accurate​ ​ result,​ ​ a​ ​ sample​ ​ size​ ​ must​ ​ be
levacccp [35]
At least 30 ..................
8 0
3 years ago
Is square meters a type of surface area
Irina18 [472]

Yes square meters is a type of surface area.

7 0
3 years ago
Could someone show me how to start this function in excel.
Mrac [35]
Attached is a screenshot of spreadsheet used to do this problem.

You will see the excel functions used for each column. The average score is highlighted in blue.

6 0
3 years ago
Helpppppppppppppppppp pls​
BartSMP [9]

Answer:

b=30

Step-by-step explanation:

The angle here is a right angle which is an angle that equals 90 degrees. You subtract that measure of the angle by 60 and you end up with 30.

7 0
3 years ago
What angle of rotation maps p onto P'?
erastovalidia [21]
Alms Alan’s Alanaj am so
7 0
3 years ago
Other questions:
  • An investment of P dollars increased to A dollars in t years. If interest was compounded continuously, find the interest rate. (
    13·1 answer
  • Which of the following is the solution to the inequality below? <br> 9-3x&gt;2(x-3)
    7·1 answer
  • Zoe and Hannah share tips in the ratio 3:7 <br> Last week ,Zoe received £24
    7·1 answer
  • PLEASE HELP!! I'm stuck on this
    15·1 answer
  • The length of an Algebra 2 textbook is 2 times the height. The sum of the length, width, and height of the box is 10 centimeters
    7·1 answer
  • EXAMPLE 3 (a) Set up the integral for the length of the arc of the hyperbola xy = 3 from the point (1, 3) to the point 6, 1 2 .
    7·1 answer
  • The arithmetic mean of 10 consecutive even integers is 3. What is the least of these 10 even integers?
    7·1 answer
  • Julie has 2 cherry lollipops, 4 lime lollipops, and 3 grape lollipops in a bag. She is going to select one lollipop, replace the
    11·1 answer
  • Can someone help me please? Ill mark brainliest c:
    6·1 answer
  • Can you guys help me solve this equation with step-by-step help, please...
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!