Question

What is the perimeter of a polygon with vertices at (−2, 1) , ​ (−2, 4) ​, (2, 7) , ​ (6, 4) ​, and (6, 1) ​?

Enter your answer in the box. Do not round any side lengths.​

Answer 1

Let A, B, C, D, E be the given points in order.
AB=4-1=3
BC=√((7-4)²+(2-(-2))²)=√(9+16)=√25=5
CD=BC=5
DE=4-1=3
AE=6-(-2)=8
Perimeter=3+5+5+3+8=24.

Answer 2

Using the distance formula, the perimeter of the polygon that has the given vertices is calculated as: 24 units.

What is the Perimeter of a Polygon?

Perimeter = sum of all sides of the polygon.

Name the vertices as follows:

• A(−2, 1)
• B​(−2, 4)
• C(2, 7)
• D(6, 4)
• E(6, 1)

Perimeter of the polygon = AB + BC + CD + DE + EA

Use the distance formula, $d = \sqrt{x_2 - x_1)^2 + (y_2 - y_1)^2}$, to find the length of each segment:

AB = |1 - 4| = 3 units

BC = √[(2−(−2))² + (7−4)²]

BC = 5 units

CD = √[(2−6)² + (7−4)²

CD = 5 units

DE = |4 - 1| = 3 units

EA = |6 - (-2)| = 8 units

Perimeter of the polygon = 3 + 5 + 5 + 3 + 8

Perimeter of the polygon = 24 units

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