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A restaurant is building an outside seating area. The owner created a map with the coordinates A(−11,11) , B(−3,11) , C(−3,1) , and D(−11,1) . Each unit on the coordinate plane represents 1 foot. Solve to find out how many feet of wall material they will need to build the new area (the perimeter).(1 point) Responses 36 feet 36 feet 80 feet 80 feet 52 feet 52 feet 40 feet

1 answer

To find the perimeter of the rectangular seating area defined by the given coordinates \(A(-11, 11)\), \(B(-3, 11)\), \(C(-3, 1)\), and \(D(-11, 1)\), we first need to calculate the lengths of the sides of the rectangle formed by these points.

  1. Calculate the length of AB:

    • Coordinates: A(-11, 11) and B(-3, 11)
    • Length of AB = \(x_B - x_A = -3 - (-11) = -3 + 11 = 8\) feet

  2. Calculate the length of AD:

    • Coordinates: A(-11, 11) and D(-11, 1)
    • Length of AD = \(y_A - y_D = 11 - 1 = 10\) feet

Since this is a rectangle, the opposite sides are equal, so:

  • Length of CD = Length of AB = 8 feet
  • Length of BC = Length of AD = 10 feet
  1. Calculate the perimeter \(P\) of the rectangle: \[ P = 2 \times (Length + Width) = 2 \times (8 + 10) = 2 \times 18 = 36 \text{ feet} \]

Thus, the total amount of wall material needed is 36 feet.

Therefore, the answer is 36 feet.