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# Area of Regions Formed by Inscribed Shapes

Lesson 5 of 37

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

#### Introduction

*10 min*

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.

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#### Problem Solving

*20 min*

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.

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#### Summary + Exit Ticket

*15 min*

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

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- LESSON 1: Explore Perimeter and Area of Composite Shapes
- LESSON 2: Perimeter of Irregular Rectilinear Shapes
- LESSON 3: Area of Composite Shapes Using a Grid
- LESSON 4: Area of Composite Shapes
- LESSON 5: Area of Regions Formed by Inscribed Shapes
- LESSON 6: CORNERSTONE:Circle Ratios: Diameter to Radius; Circumference to Diameter
- LESSON 7: CORNERSTONE: Circumference Formula
- LESSON 8: Area of a Circle
- LESSON 9: Circumference & Area Fluency Practice
- LESSON 10: Finding the Radius From a Given Circumference or Area
- LESSON 11: Circumference from Area / Area from Circumference
- LESSON 12: Circle Designs: Finding the Area and Perimeter of Shapes Composed of Arcs and Line Segments
- LESSON 13: Assessment_Area and Perimeter (Circumference) of Composite Shapes and Circles
- LESSON 14: Drawing Prisms & Pyramids
- LESSON 15: Describe Prisms and Pyramids Using Algebra
- LESSON 16: Using Nets to Find the Surface Area of Prisms
- LESSON 17: Using a Formula to Find the Surface Area of Prisms
- LESSON 18: Finding the surface area of triangular prisms using a net
- LESSON 19: Finding the Surface Area of a Triangular Prism Using A Formula
- LESSON 20: Discovering the Formula for the Surface Area of A Cylinder
- LESSON 21: Finding the Surface Area of Cylinders Using a Formula
- LESSON 22: Practice Day: Surface Area of Prisms & Cylinders
- LESSON 23: Surface Area of Prisms and Cylinders Assessment
- LESSON 24: Finding the Surface Area of Pyramids Using Nets
- LESSON 25: Finding the Surface Area of Pyramids Using a Formula
- LESSON 26: Surface Area of Composite Shapes
- LESSON 27: Surface Area of Composite Shapes With Holes
- LESSON 28: Surface Area Assessment
- LESSON 29: 3-D Models from 2-D Views
- LESSON 30: Exploring Volume and Surface Area with Unifix Cubes
- LESSON 31: Explore Volume of Rectangular Prisms
- LESSON 32: Find the Volume of Prisms Using a Formula
- LESSON 33: Volume Of Cylinders Using a Formula
- LESSON 34: Volume of Composite Shapes
- LESSON 35: Volume and Surface Area - Accelerated Math Fluency Day
- LESSON 36: Volume of Pyramids
- LESSON 37: Surface Area and Volume Final Assessment