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Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

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**

- 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. - Calculate the area and perimeter of the given quadrilateral using the shoelace formula.
- Break up the pentagon to find the area using Green’s theorem. Compare your method with a partner.
- Find the perimeter and the area of the quadrilateral with vertices 𝐴(−3, 4), 𝐵(4, 6), 𝐶(2,−3), and 𝐷(−4,−4).
- Find the area of the pentagon with vertices 𝐴(5, 8), 𝐵(4,−3), 𝐶(−1,−2),𝐷(−2, 4), and 𝐸(2, 6).
- Find the area and perimeter of the hexagon shown.

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