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) 24 units
B) 12 units
C) 64 units
D) 32 units

Answer 1

To find the perimeter of the polygon ABCD with given vertices, we calculate the lengths of the sides and sum them up. Therefore, the perimeter of the polygon ABCD is 4 + 8 + 4 + 8 = 24 units.

Step-by-step explanation:

To find the perimeter of the polygon ABCD, we need to sum up the lengths of all the sides.

The given vertices are A(2,-2), B(6, -2), C(6, 6), and D(2, 6).

Using the distance formula, we calculate the lengths of the sides:

AB = sqrt((6 - 2)^2 + (-2 - (-2))^2) = sqrt(16 + 0) = 4

BC = sqrt((6 - 6)^2 + (6 - (-2))^2) = sqrt(0 + 64) = 8

CD = sqrt((2 - 6)^2 + (6 - 6)^2) = sqrt(16 + 0) = 4

AD = sqrt((2 - 2)^2 + (6 - (-2))^2) = sqrt(0 + 64) = 8

Therefore, the perimeter of the polygon ABCD is 4 + 8 + 4 + 8 = 24 units.