Question

What is the perimeter of polygon ABCD?

Answer 1

Answer: 36 lol

Explanation:

Answer 2

The perimeter is the sum of the length of the sides of a certain shape. In this case, the perimeter of the polygon would be the sum of the lengths of sides AB, BC, CD, and DA.

Explanation:

Lets start computing the length of each side of the polygon. Using points A and B as a first example, we find that the distance between them will be:

`d_(AB)=√((x_A - x_B) ^2+(y_A - y_B) ^2 )`

Where
`(x_A , y_A )` and
`(x_B , y_B )` are the coordinates of points A and B respectively.

From the graph we can see that point A has coordinates (5, 12), B has coordinates (9, 9), C has coordinates (12, 5), and D has coordinates (0, 0). Puting values and computing the lengths we find that:

Lenght AB:

`d_(AB)=√((x_A - x_B) ^2+(y_A - y_B) ^2)=√((5 - 9) ^2+(12 - 9) ^2)`

`d_(AB)=√((-4) ^2+(3) ^2 ) =√(16 + 9 )=√(25)`

`d_(AB)=5`

Lenght BC:

`d_(BC)= √((x_B - x_C) ^2 + (y_B - y_C) ^2 ) = √((9 - 12) ^2 + (9 - 5) ^2 )`

`d_(BC)=√((-3) ^2 + (4) ^2 )=√(9 + 16 ) =√(25)`

`d_(BC)=5`

Lenght CD:

`d_(CD)= √((x_C - x_D) ^2 + (y_C - y_D) ^2 ) = √((12 - 0) ^2 + (5 - 0) ^2 )`

`d_(CD)=√((12) ^2 + (5) ^2 ) = √(144 + 25 ) = √(169)`

`d_(CD)=13`

Lenght DA:

`d_(DA)= √((x_D - x_A) ^2 + (y_D - y_A) ^2 ) = √((0 - 5) ^2 + (0 - 12) ^2 )`

`d_(DA)=√((-4) ^2 + (-12) ^2 ) = √(25 + 144 ) = √(169)`

`d_(DA)=13`

Therefor the result will be:

`Perimeter = d_(AB) + d_(BC) +d_(CD) +d_(DA)= 5 + 5 + 13 + 13 = 36`