- Author:
- Mark Freed
- Subject:
- Mathematics, Geometry
- Material Type:
- Activity/Lab
- Level:
- High School
- Tags:

- License:
- Creative Commons Attribution Non-Commercial
- Language:
- English
- Media Formats:
- Downloadable docs

# Area of Irregular Shapes Worksheet

# Area of Irregular Shapes

## Overview

Overview: Math in Real Life (MiRL) supports the expansion of regional networks to create an environment of innovation in math teaching and learning. The focus on applied mathematics supports the natural interconnectedness of math to other disciplines while infusing relevance for students. MiRL supports a limited number of networked math learning communities that focus on developing and testing applied problems in mathematics. The networks help math teachers refine innovative teaching strategies with the guidance of regional partners and the Oregon Department of Education.

# Lesson Overview

# Introduction

Students will be able find a scale from the top view of the building and the actual view. Using this scale, they will calculate the perimeter and area of the roof of the building and calculate the costing of supplies needed for this roof.

-Prerequisite: lessons on perimeter and are of rectangles, squares

# Materials

- Drone and iPad
- Alternate: Satellite Image from publically available website.

- Video of flight of drone over building of choice with irregular shape.
- Copies of the top view of building (preferably in color).
- Tape measure, yard or meter stick.
- Copies of “Area of Irregular Shapes Task Worksheet.”

# Time Required

- 1-2 classroom periods.

# Authors

- Victor Woods

# Standards

- HSG.MG.A.1 Use geometric shapes, their measures, and their properties to describe objects (e.g. Modeling a tree trunk or a human torso as a cylinder).
- HSG.MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

# Practice Standards

- HS.F.MP.1 Make sense of problems and persevere in solving them.
- HS.F.MP.2 Reason abstractly and quantitatively.
- HS.F.MP.3 Construct viable arguments and critique the reasoning of others.
- HS.F.MP.4 Model with mathematics.
- HS.F.MP.5 Use appropriate tools strategically.
- HS.F.MP.6 Attend to precision.
- HS.F.MP.7 Look for and make use of structure.
- HS.F.MP.8 Look for and express regularity in repeated reasoning

# LAUNCH - SET UP

# Anticipated Time:

- 20 minutes

# Suggested Grouping:

- Individual Student Work

# Teacher Questions and Actions:

- Take class outside and demonstrate how to use drone to fly over designated building and video flight.
- Demonstrate how to take a picture of the overhead view of an object.
- Return to class; divide the class into groups of 2-3 students.
- Pass out worksheet, “Area of Irregular Shapes” and picture of the top view of the high school.

The Problem:

You are asked to come up with a cost analysis of tarring the high school root and to replace the edging along the roofs edge. The edging costs $1.75 per linear foot and a gallon of tar is $7.99 per gallon. A gallon of tar cover 40 ft^{2 }of roofing. Find the total cost to maintain the high school roof.

# Anticipated Student Responses/Issues:

- Have the students brainstorm ideas how to find the actual dimensions of the building from the picture.
- You may have to lead them to scale and scale factor of the picture to the actual size.
- How are you going to chunk up the surface?

# EXPLORE - INVESTIGATE

# Anticipated Time:

- 25 minutes

# Suggested Grouping:

- Collaborative Small Group Work

# Teacher Questions and Actions:

Students should have completed the worksheet by:

1. Identifying the scale factor they used.

2. Calculations shown for area and perimeter of the building’s roof.

3. Calculations for the cost analysis of the tar and edging of the roof.

4. Calculations for the total cost of the project.

5. Explanations for each part explaining how they got their findings.