Question

Find the perimeter of the polygon ABCD that has its vertices at A(2, –2), B(6, –2), C(6, 6), and D(2, 6).

a) 64 units
b) 32 units
c) 24 units
d) 12 units

Answer 1

To find the perimeter of the polygon ABCD, calculate the length of each side and add them up. The perimeter of the polygon ABCD is 24 units.

Step-by-step explanation:

To find the perimeter of the polygon ABCD, we need to calculate the length of each side of the polygon and add them up. Here are the steps:

1. Calculate the length of side AB using the distance formula: AB = sqrt((6-2)^2 + (-2-(-2))^2) = 4 units
2. Calculate the length of side BC using the distance formula: BC = sqrt((6-6)^2 + (6-(-2))^2) = 8 units
3. Calculate the length of side CD using the distance formula: CD = sqrt((2-6)^2 + (6-6)^2) = 4 units
4. Calculate the length of side DA using the distance formula: DA = sqrt((2-2)^2 + (-2-6)^2) = 8 units
5. Add up the lengths of all sides: AB + BC + CD + DA = 4 + 8 + 4 + 8 = 24 units

Therefore, the perimeter of the polygon ABCD is 24 units, so the correct answer is option c) 24 units.