Figure abcde is a regular pentagon. segment ae is located at a (2, 1) and e (4, 1). what is the perimeter of abcde? 4 units 6 units 8 units 10 units

The perimeter of ABCDE is 10 units

Step-by-step explanation:

* Lets talk about the regular pentagon

- The regular pentagon has five equal sides

- It has five equal angles

- The measure of each interior angle is = 108°

- The perimeter of it = 5 × length of one side

- To find the length of a side whose endpoints are (x1 , y1) , (x2 , y2)

  is √[(x2 - x1)² + (y2 - y1)²]

- If x1 = x2, then the line is vertical and its length = y2 - y1

- If y1 = y2, then the line is horizontal and its length = x2 - x1

* Now lets solve the problem

∵ ABCDE is a regular pentagon

- All of its sides are equal in length

∴ AB = BC = CD = DE = EA

∵ A = (2 , 1) and E = (4 , 1)

- The y-coordinates of points A and E are equal, then AE is horizontal

∵ The y-coordinates of point A and E = 1

∴ AE is a horizontal side

∴ Its length = x2 - x1

∵ x2 = 4 , x1 = 2

∴ The length of AE = 4 - 2 = 2 units

- The perimeter of the regular pentagon = 5 × length of one side

∴ Its perimeter = 5 × 2 = 10 units

* The perimeter of ABCDE is 10 units

why can't you?

step-by-step explanation:

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