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
Rufina [12.5K]
2 years ago
13

Identify the polygon with vertices A(5,0), B(2,4), C(−2,1), and D(1,−3), and then find the perimeter and area of the polygon. HE

LP ASAP!

Mathematics
1 answer:
inn [45]2 years ago
6 0

Answer:

Part 1) The polygon is a square

Part 2) The perimeter is equal to 20\ units

Part 3) The area is equal to 25\ units^{2}

Step-by-step explanation:

we have

A(5,0), B(2,4), C(-2,1),D(1,-3)

Plot the points

see the attached figure

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

Find the distance AB

A(5,0),B(2,4)

substitute in the formula

d=\sqrt{(4-0)^{2}+(2-5)^{2}}

d=\sqrt{(4)^{2}+(-3)^{2}}

d=\sqrt{25}

AB=5\ units

Find the distance BC

B(2,4), C(-2,1)

substitute in the formula

d=\sqrt{(1-4)^{2}+(-2-2)^{2}}

d=\sqrt{(-3)^{2}+(-4)^{2}}

d=\sqrt{25}

BC=5\ units

Find the distance CD

C(-2,1),D(1,-3)

substitute in the formula

d=\sqrt{(-3-1)^{2}+(1+2)^{2}}

d=\sqrt{(-4)^{2}+(3)^{2}}

d=\sqrt{25}

CD=5\ units

Find the distance AD

A(5,0),D(1,-3)

substitute in the formula

d=\sqrt{(-3-0)^{2}+(1-5)^{2}}

d=\sqrt{(-3)^{2}+(-4)^{2}}

d=\sqrt{25}        

AD=5\ units

we have that

AB=BC=CD=AD

Find the distance BD (diagonal)

B(2,4),D(1,-3)

substitute in the formula

d=\sqrt{(-3-4)^{2}+(1-2)^{2}}

d=\sqrt{(-7)^{2}+(-1)^{2}}

BD=\sqrt{50}\ units        

<em>Verify if the polygon is a square</em>

If the triangle BDA is a right triangle, then the polygon is a square

Applying the Pythagoras theorem

BD^{2}=AD^{2}+AB^{2}

substitute

(\sqrt{50})^{2}=5^{2}+5^{2}

50=50 -----> is true

so

The triangle BDA is a right triangle

therefore

The polygon is a square

<em>Find the Area of the polygon</em>

The area of a square is equal to

A=b^{2}

we have

b=5\ units

A=5^{2}=25\ units^{2}

<em>Find the perimeter of the polygon</em>

The perimeter of a square is equal to

P=4b

we have

b=5\ units

P=4(5)=20\ units

You might be interested in
1500+1500 please answer
ehidna [41]
3000 is the freaking right answer
7 0
3 years ago
Read 2 more answers
So sad but so true do you think so ???
Inessa05 [86]

Answer:

AWWWWW :( SOOOOO SAD!!!

Step-by-step explanation:

BUT TRU UNFORINATLEY

6 0
3 years ago
Read 2 more answers
The area of a rectangle is 72 cm square. The length of the rectangle is 6 cm longer than the width. What is the width of the rec
tangare [24]
The answer is B: 6 cm. You can use guess-and-check method, and plug the possible different answers into the equation x(x+6)=72, x stands for the width.
4 0
3 years ago
Which does NOT represent a function? ill give brainliest
r-ruslan [8.4K]

Answer:

C

Step-by-step explanation:

C is not a function because 5 has two y values

8 0
2 years ago
Read 2 more answers
In a statistics​ class, the standard deviation of the heights of all students was 3.8 inches. The standard deviation of the heig
goblinko [34]

Answer:

The reason why standard deviation of the entire class is greater than standard deviation of males and females considered separately, is that mean values for males and females are different from each other.

Step-by-step explanation:

The concept of mean is well represented by the following formula

mean = \frac{(x1 + x2 + x3 + ..... + xn)}{N}, where x1, x2, xn are the observations and N is the number of observations (population).

Standard deviation represents the distance between each observation and the mean of the population (all observations). The formula for this parameter is:

Standard deviation =√[((x1 - x)² + (x2-x)² + ....+ (xn-x)²)/N-1], where x1, x2,..., xn are the observations and x is the mean value.

In this case you have that each height registered is an observation and the number of observations represents the N value. As you can see if the mean for males is different from that of females their standard deviation will be different too. Usually males have heigths greater than that of females (1.77 vs 1.64, in USA for example), and heights inside each group will be more similar than between groups. Then, when you mix all observation there will be an increase in standard deviation, because you are mixing very different heigths

4 0
3 years ago
Other questions:
  • Addition and subtraction facts for the number 358
    7·2 answers
  • A box of candy has 21 pieces total of 7 of the pieces are cherry flavored what is the ratio of other flavors to the cherry flavo
    5·2 answers
  • a frog made three jumps. The first was 12 5/6 inches. The second jump was 8 3/6 inches.the third jump was 15 1/6 inches. What wa
    7·1 answer
  • A company sells kitchen toys for kids, including artificial carrots that are cone shaped with a radius of 1 cm and a height of 6
    14·1 answer
  • What number multiplied by itself 3 times equals 10
    6·1 answer
  • Help me plz!!!!!!!!!!!!!!!!!!!!
    14·1 answer
  • 2. Eliza uses the point (3, 9) to her home’s location and uses the point (6, 13) to represent the ice cream shop’s location. Eac
    12·1 answer
  • Round 58.9871 2 decimal place
    8·1 answer
  • Please answer I don’t understand this at all. And I’m not falling for those links
    13·1 answer
  • The figure shown has two parallel lines cut by a transversal:
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!