Question

Look at the square ABCD Below.
A(-2, 0), B(0,6 ), C(6,4) and D(4, -2)
What is it's perimeter?

Answer 1

To find the perimeter of the square ABCD, we need to find the distance between each pair of consecutive points and then add them up.

Using the distance formula:

Distance between A and B:
AB = √[(0 - 0)^2 + (6 - 0)^2] = √(0 + 36) = √36 = 6

Distance between B and C:
BC = √[(6 - 0)^2 + (4 - 6)^2] = √(36 + 4) = √40

Distance between C and D:
CD = √[(4-6)^2 + (-2 - 4)^2] = √(4 + 36) = √40

Distance between D and A:
DA = √[(-2-4)^2 + (0 + 4)^2] = √(36 + 16) = √52

Now, add up the distances to find the perimeter:
Perimeter = AB + BC + CD + DA
Perimeter = 6 + √40 + √40 + √52
Perimeter ≈ 6 + 12.65 + 12.65 + 7.21
Perimeter ≈ 38.51 units

Therefore, the perimeter of the square ABCD is approximately 38.51 units.