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
A woman paid $28 per a dress. She bought 6 dresses. How much money did the woman spend on dresses?
Tju [1.3M]

Answer:

$168

Step-by-step explanation:

28x6

= 168

4 0
2 years ago
Read 2 more answers
The right triangle on the right is a scaled copy of the right triangle on the left. Identify
AlekseyPX

Answer:

scale factor is 1:3.5

Step-by-step explanation:

56/16 = 3.5

5 0
2 years ago
Read 2 more answers
HELP PLEASE <br> What is the area of the kite below?
Kryger [21]

Answer:

Area = 33 inches squared

Step-by-step explanation:

The formula for the area of a kite is:

Area = ½ × (d)1 × (d)2

To find the first diagonal (d1):

d1 = 7 in + 4 in = 11 in

To find the second diagonal (d2):

The triangles on the right of the kite must be 3 4 5 triangle since it is a right triangle with a hypotenuse of 5 and a side of 4, we know half of a diagonal would be 3 inches.

d2 = 3 in + 3 in = 6 in

Now we can plug the diagonals into the area formula.

Area = ½ × 11 × 6 = 33 inches squared

6 0
2 years ago
Read 2 more answers
Which facts could be applied to the simplified expression. Check all that apply. 5x+3y+(-x)+62
Anettt [7]

Answer:

4x+3y+62

Step-by-step explanation:

the other variables wouldnt be able to do anything to 62 because they are different variables.

7 0
3 years ago
Read 2 more answers
Which statement describes the value of the expression 4 * 18932 + 921
IceJOKER [234]
I'm confused, there are no statement. 
But <span>4 * 18932 + 921 is equal to 76,649.

4*18932+921
75728+921= 76649
</span>
8 0
3 years ago
Other questions:
  • Please Help image below
    11·1 answer
  • in July ,gas price increse by 15%. in agust , they decrease by 10%. what is the total percent change since june
    5·1 answer
  • there are 32 forwards and 80 guards in leos basketball league. eo must include all players on a team and wants each team to have
    12·2 answers
  • Analyze the equation below and complete the instructions that follow.
    10·2 answers
  • Write a real world problem where you would have to multiply 120 and 75.
    5·1 answer
  • The seventh grade haa a new music teacher Ms. Fritz. Some students have learned a great deal from her, but others think she teac
    15·2 answers
  • Andre is reviewing proportional relationships. He wants to practice using a graph that goes through a point so that each X-coord
    9·2 answers
  • Which statement is true about the given function?
    14·1 answer
  • The distance , d, a train travels in miles depends on the hours, h. The equation shows this relationship, d=120h. How many miles
    11·1 answer
  • I’m on my post quiz please help!!
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!