To solve the problem and determine the perimeter of the quadrilateral in the image, we will calculate the lengths of each segment and sum them up. Here's how:

1. Identify the vertices: From the graph, the vertices are approximately located at:

   • $(-6, 3)$
   • $(2, 3)$
   • $(2, -6)$
   • $(-6, -6)$

2. Calculate the lengths of the segments: Use the distance formula for diagonal sides and observe the grid spacing for vertical or horizontal sides.

The distance formula is: $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Let me calculate these lengths.import math

Coordinates of the vertices

vertices = [(-6, 3), (2, 3), (2, -6), (-6, -6)]

Function to calculate distance between two points

def distance(point1, point2): return math.sqrt((point2[0] - point1[0])**2 + (point2[1] - point1[1])**2)

Calculate lengths of each side

side1 = distance(vertices[0], vertices[1]) # Horizontal top side2 = distance(vertices[1], vertices[2]) # Vertical right side3 = distance(vertices[2], vertices[3]) # Horizontal bottom side4 = distance(vertices[3], vertices[0]) # Vertical left

Total perimeter

perimeter = side1 + side2 + side3 + side4 perimeter_rounded = round(perimeter, 1)

side1, side2, side3, side4, perimeter_rounded(8.0, 9.0, 8.0, 9.0, 34.0)(8.0, 9.0, 8.0, 9.0, 34.0)successThe lengths of the sides of the quadrilateral are:

• Top horizontal side: $8.0$ units
• Right vertical side: $9.0$ units
• Bottom horizontal side: $8.0$ units
• Left vertical side: $9.0$ units

The total perimeter of the quadrilateral is $34.0$ units.

It seems the correct answer is not listed in the options provided. Let me know if you need further clarification or assistance! Here are some related questions for practice:

1. How do you calculate the area of this quadrilateral?
2. What is the distance between the diagonal endpoints of the quadrilateral?
3. How do you derive the equation of the diagonal lines within the shape?
4. What is the midpoint of each side of the quadrilateral?
5. How would the perimeter change if the shape were scaled by a factor of 2?

Tip: Always double-check the placement of vertices on a graph when calculating lengths!