Explain how you can use estimation to check that your answer is reasonable

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

inn [45]

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

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

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

$BD=\sqrt{50}\ units$

Verify if the polygon is a square

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

Find the Area of the polygon

The area of a square is equal to

$A=b^{2}$

we have

$b=5\ units$

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

Find the perimeter of the polygon

The perimeter of a square is equal to

$P=4b$

we have

$b=5\ units$

$P=4(5)=20\ units$

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3 years ago

Which is a nonrigid transformation of f(x)?

lianna [129]

Nonrigid transformation changes the size but not the shape.

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3 years ago

Diana has just begun the process of filing her federal income tax return, and she plans to deduct medical and dental expenses. w

Andru [333]

Answer:

1040 tehyimngtumh

Step-by-step explanation:

Apex

5 0

3 years ago

If x^ 3 = -27, then what is x?

wariber [46]

The cube root of -27 is -3

3√-27 = -3

You can check this by plugging your answer back it

X= -3

-3^3 = -27

7 0

3 years ago

Read 2 more answers

The lateral surface area of cone A is exactly 1/2 the lateral surface area of cylinder B. Cone A radius is r and height h - Cyli

Mrac [35]

The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to $r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}$ . (Correct choice: False)

<h3>What is the ratio of lateral area of cone to the lateral area of the cylinder?</h3>

In accordance with space geometry, the lateral areas of the cone and cylinder are described by the following equations:

Cone

$A_{l} = \pi \cdot r \cdot \sqrt{r^{2}+h^{2}}$ (1)

Cylinder

$A_{l} = 2\pi\cdot r\cdot h$ (2)

If we divide (2) by (1), then we have the following ratio:

$r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}$

The ratio of the lateral surface area of cone A to the lateral surface area of cylinder B is equal to $r = \frac{1}{2}\cdot \frac{\sqrt{r^{2}+h^{2}}}{h}$ . (Correct choice: False)

To learn more on surface areas: brainly.com/question/2835293

#SPJ1

3 0

2 years ago