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HELP FAST 100 POINTS
Calculate the perimeter of parallelogram ABCD. Show all work.

HELP FAST 100 POINTS Calculate The Perimeter Of Parallelogram ABCD Show All Work class=

Sagot :

caylus

Answer:

Hello,

Step-by-step explanation:

[tex]|AD|^2=(3-(-1))^2+(0-(-1))^2=16+1=17\\\\|AB|^2=1^2+3^2=10\\\\\boxed{Perimeter=2*\sqrt{17} +2*\sqrt{10}}[/tex]

Answer:

2*√10 + 2*√17

Step-by-step explanation:

In order to find the perimeter we must find the length of each side

To find the length of the sides we must use the distance formula

Distance formula:

d = √ ( x2 - x1 )² + ( y2 - y1 )²

Where the x and y values are derived from the points of each side

First let's find the length of AB

Coordinates of A: (-1,-1)

Coordinates of B: (0,2)

* Define variables *

( Remember coordinates are written as (x,y))

x1 = -1

x2 = 0

y1 = -1

y2 = 2

Now to find the length of AB we simply plug in the values of x and y into the distance formula

d = √ ( x2 - x1 )² + ( y2 - y1 )²

x1 = -1, x2 = 0, y1 = -1, y2 = 2

* Plug in values *

d = √(0 - (-1))² + (2 - (-1))

If there are two negative signs in front of a number then the two negative signs cancel out and the sign changes to +

d = √(0+1)² + (2+1)²

Simplify addition

d = √(1)² + (3)²

Apply exponents

d = √1 + 9

Simplify addition

d = √10

So the length of AB is √10

One of the properties of a parallelogram is that the opposite sides are congruent.

So the opposite side of AB (CD) is also equal to √10

Next we need find the length of AD

We use the same process we used for finding the length of AB

Coordinates of A: (-1,-1)

Coordinates of D: (3,0)

*Define variables*

x1 = -1

x2 = 3

y1 = -1

y2 = 0

Plug in the values of x and y into the formula ( formula is d = √ ( x2 - x1 )² + ( y2 - y1 )² )

*Plug in the values of x and y )

d = √( -1 - 3 )² + ( 0 - (-1)²

Simplify subtraction and addition

d = √(-4)² + (1)²

Apply exponents

d = √16 + 1

Add

d = √17

So the length of AD is √17

Like stated previously opposite sides in a parallelogram are congruent so the opposite side of AD (BC) also has a length of √17

Now to find the perimeter,

The perimeter is the sum of the side lengths

Side lengths of the parallelogram shown:

AB = √10

BC = √17

CD = √10

DA = √17

Perimeter = √10 + √17 + √10 + √17 = 2*√10 + 2*√17

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