Final answer:
The perimeter of rectangle ABCD is 24 units and the area is 35 square units, calculated using the coordinates of the vertices and the distance formula.
Step-by-step explanation:
To find the perimeter and area of rectangle ABCD, with vertices A(-4,-6), B(-4,-1), C(3,-1), and D(3,-6), we can use the distance formula for the coordinates. The perimeter of a rectangle is the sum of all its sides times 2 because opposite sides are equal in length. The area of a rectangle is the product of its length and width.
To determine the lengths of the sides, observe that AB and CD are vertical sides, so their length is the difference in the y-coordinates, which is |-1 - (-6)| = 5 units. Similarly, BC and AD are horizontal sides, so their length is the difference in the x-coordinates, which is |3 - (-4)| = 7 units.
Having determined the lengths of the sides, we can now calculate the perimeter as P = 2(l + w) = 2(5 + 7) = 24 units. The area is A = l × w = 5 × 7 = 35 square units. Thus, the perimeter of rectangle ABCD is 24 units and the area is 35 square units.