# Perimeter and Area of Polygonal Regions in the Cartesian Plane

### New York State Common Core Math Geometry, Module 4, Lesson 10

Worksheets for Geometry, Module 4, Lesson 10

Student Outcomes

• Students find the perimeter of a quadrilateral in the coordinate plane given its vertices and edges.
• Students find the area of a quadrilateral in the coordinate plane given its vertices and edges by employing Green’s theorem.

Perimeter and Area of Polygonal Regions in the Cartesian Plane

Classwork

Opening Exercise

Find the area of the triangle given. Compare your answer and method to your neighbor’s, and discuss differences

Exercises

1. Given rectangle 𝐴𝐵𝐶𝐷:
a. Identify the vertices.
b. Find the perimeter using the distance formula.
c. Find the area using the area formula.
d. List the vertices starting with 𝐴 moving counterclockwise.
e. Verify the area using the shoelace formula.
2. Calculate the area and perimeter of the given quadrilateral using the shoelace formula.
3. Break up the pentagon to find the area using Green’s theorem. Compare your method with a partner.
4. Find the perimeter and the area of the quadrilateral with vertices 𝐴(−3, 4), 𝐵(4, 6), 𝐶(2,−3), and 𝐷(−4,−4).
5. Find the area of the pentagon with vertices 𝐴(5, 8), 𝐵(4,−3), 𝐶(−1,−2),𝐷(−2, 4), and 𝐸(2, 6).
6. Find the area and perimeter of the hexagon shown.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.