Question

a quadrilateral has vertices (3, 6), (7, 6), (11, 3), and (3, 3). what is the perimeter of the quadrilateral?
□ units

Explanation:

Step1: Find length of horizontal/vertical sides

• Between (3,6) and (7,6): horizontal, length $7 - 3 = 4$.
• Between (3,6) and (3,3): vertical, length $6 - 3 = 3$.
• Between (3,3) and (11,3): horizontal, length $11 - 3 = 8$.

Step2: Find length of slant side (7,6) to (11,3)

Use distance formula $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$.
Here, $x_1 = 7, y_1 = 6, x_2 = 11, y_2 = 3$.
$d = \sqrt{(11 - 7)^2 + (3 - 6)^2} = \sqrt{4^2 + (-3)^2} = \sqrt{16 + 9} = \sqrt{25} = 5$.

Step3: Sum all side lengths

Perimeter = $4 + 3 + 8 + 5 = 20$.

Answer:

20