Perimeter and Area on the Coordinate Plane
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This learning activity provided by:
Author:
Adriane Howard
System: Tuscaloosa City School: Paul W Bryant High School
General Activity Information
Activity ID:
2542
Title: Perimeter and Area on the Coordinate Plane
Digital Tool/Resource: Geogebra
Web Address – URL:
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.
Associated Standards and Objectives
Content Standard(s):
Mathematics 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.
Unpacked Content
Evidence Of Student Attainment:
Students:
Given the coordinates of the vertices of a polygon,
Use the distance formula to find the measure of the sides to aide in computing the perimeter and area using a variety of methods. Methods may include:
Using the distance formula to find the length of each side.
Using slopes of perpendicular lines to determine when a side of a triangle or
quadrilateral may be used as the height.
Using a system of equations and the distance formula to find the height of a
non right triangle.
Using geometry software such as geogebra.org to find the perimeter and area of polygons to aide in the accuracy of results. Teacher 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. Diverse Learning Needs:
Essential Skills:
Learning Objectives: GEO.18.1: Define area, perimeter, regular polygons, inscribed polygons, circumscribed polygons, and vertices.
GEO.18.2: Analyze the given information to develop a logical process to calculate area or perimeter.
GEO.18.3: Create equations for area and perimeter based on given information.
GEO.18.4: Illustrate graphically an inscribed or circumscribed polygon.
GEO.18.5: Solve equations given the area and perimeter.
GEO.18.6: Plot given coordinates on the Cartesian plane.
Prior Knowledge Skills:
Define quadrant, coordinate plane, coordinate axes (x-axis and y-axis), horizontal, vertical, and reflection.
Demonstrate an understanding of an extended coordinate plane.
Draw and label a 4 quadrant coordinate plane.
Draw and extend vertical and horizontal number lines.
Interpret graphing points in all four quadrants of the coordinate plane in real-world situations.
Recall how to graph points in all four quadrants of the coordinate plane.
Define area.
Analyze the area of other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes.
Apply area formulas to solve real-world mathematical problems.
Demonstrate how the area of a rectangle is equal to the sum of the area of two equal right triangles.
Explain how to find the area for rectangles.
Select manipulatives to demonstrate how to compose and decompose triangles and other shapes.
Recognize and demonstrate that two right triangles make a rectangle.
Define vertices.
Apply absolute value to find the length of a side joining points with the same first coordinate or the same second coordinate.
Plot points on a coordinate plane., then connect points for the vertices to sketch a polygon.
Identify ordered pairs.
Recognize polygons.
Define perimeter and area.
Identify the length between vertices on a coordinate plane.
Calculate the perimeter and area using the distance between the vertices.
Alabama Alternate Achievement Standards
AAS Standard:
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.
Strategies, Preparations and Variations
Phase: During/Explore/Explain
Activity:
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.
Advanced Preparation:
Students will need internet access and a device.
Handouts may be printed or shared with students using a digital platform such as Google Classroom.
Variation Tips (optional): 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.
Notes or Recommendations (optional):
Keywords and Search Tags
Keywords and Search Tags:
area, coordinate plane, distance formula, dynamic software, perimeter
