Geometry.4.C.10 - Perimeter and Area of Polygonal Regions in the Cartesian Plane – Exit Ticket

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Use the following image to answer the question below.

Cory is using the shoelace formula to calculate the area of the pentagon shown. The pentagon has vertices A(4, 7), B(2, 5),C(1, 2), D(3, 1), and E(5, 3). His calculations are below. Toya says his answer can’t be correct because the area in the region is more than 2 square units. Can you identify and explain Cory’s error and help him calculate the correct area?

From EngageNY.org of the New York State Education Department. Grade Geometry Mathematics Module 4, Topic C, Lesson 10. Internet. Available from https://www.engageny.org/resource/geometry-module-...; accessed 14/Apr/2016.