Perimeter and Area on the Coordinate Plane

Learning Resource Type

Learning Activity

Subject Area

Mathematics

Grade(s)

9, 10, 11, 12

Overview

In this lesson, students will use the distance formula and dynamic geometry software to compute the perimeter and area of polygons. Students will use the distance formula to calculate the length of each side of the given polygon.  Students will then compute the perimeter and area of each polygon.  All computations will be verified using a Geogebra applet.

This activity results from the ALEX Resource Development Summit.

Phase

During/Explore/Explain
Mathematics (2019) Grade(s): 09-12 - Geometry with Data Analysis

MA19.GDA.18

Given the coordinates of the vertices of a polygon, compute its perimeter and area using a variety of methods, including the distance formula and dynamic geometry software, and evaluate the accuracy of the results.

UP:MA19.GDA.18

Vocabulary

  • Coordinates
  • vertices
  • perimeter
  • Area
  • Distance formula
  • Evaluate
  • Accuracy

Knowledge

Students know:
  • The distance formula and its applications.
  • Techniques for coordinate graphing.
  • Techniques for using geometric software for coordinate graphing and to find the perimeter and area.

Skills

Students are able to:
  • Create geometric figures on a coordinate system from a contextual situation.
  • Accurately find the perimeter of polygons and the area of polygons such as triangles and rectangles from the coordinates of the shapes.
  • Explain and justify solutions in the original context of the situation.

Understanding

Students understand that:
  • Contextual situations may be modeled in a Cartesian coordinate system.
  • Coordinate modeling is frequently useful to visualize a situation and to aid in solving contextual problems.

Learning Objectives

Students will use coordinates to compute perimeters of polygons and areas of triangles and rectangles using the distance formula and dynamic geometry software.

Activity Details

  • Using the Perimeter and Area on the Coordinate Plane - Geogebra Handout, students will work independently as they calculate the lengths of each side of the given polygons.
  • After they have completed their calculations, students may compare results with their seat partners.
  • Students will use their measurements to calculate the perimeters of each polygon.
  • Students will also use their measurements to calculate the area of each triangle and rectangle.
  • All students will need to verify their computations using the Geogebra applet.

Assessment Strategies

The teacher can allow students to work on one polygon at a time, and utilize Think-Pair-Share as a formative assessment to check for student understanding.

Background / Preparation

Teachers may need to customize the GeoGebra toolbar if students are unfamiliar with the dynamic software tools, by selecting only tools students will use for the activity.

Total Duration

16 to 30 Minutes

Learning Activity (During)

Materials and Resources

Internet access
Digital device
Online Learning Platform (i.e. Google Classroom, Canvas, Schoology, etc)

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