# Area of Regions Formed by Inscribed Shapes

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## Objective

SWBAT find the area of regions formed by inscribed shapes by problem solving

#### Big Idea

Students solve all the problems by first graphing the shapes on a coordinate grid.

## Introduction

10 minutes

I will have the results of an image search for “inscribed shapes” on the SmartBoard.  I will ask students to think about what is unique about each shape (they involve inscribed shapes) and how do they differ from the shapes from the previous day.  Again here is a great opportunity for students to practice precision in language (MP6) as they describe the various shapes.  We will define the term inscribed shapes.  Next I will ask the essential question while showing the exit ticket problem.  We will not discuss answers.

## Problem Solving

20 minutes

I will explain the instructions for plotting the shapes.  Make sure students are using pencils or erasable ink because it is easy to make simple plotting errors. I’ll have students graph all points first before making the shapes.  I’ll insist that students use rulers to make straight line segments.

Students work on finding the area for 8 problems.  They may discuss their work with their row partners.  When students are stuck on how to find a shaded region, the teacher should not directly answer the question, but should instead ask questions that could lead to an answer (ie “What is the area of the entire shape?  What is the area of the inscribed shape?  What part of the entire shape is shaded?  What shapes are present?").  These questions should focus students attention on the component parts of the shape. (MP7)

Problem 3 is a square whose vertices are on the axes.  Students may need to think of this as 2 triangles in order to find the area, unless they are already familiar with the Pythagorean Theorem.

## Summary + Exit Ticket

15 minutes

Students present solutions framed around the essential question.  We conclude that subtracting the areas of the outer shape and the inscribed shape results in the area of the shaded region. Students then take an exit ticket