Lesson 11Polygons
Learning Goal
Let’s investigate polygons and their areas.
Learning Targets
I can describe the characteristics of a polygon using mathematical vocabulary.
I can reason about the area of any polygon by decomposing and rearranging it, and by using what I know about rectangles and triangles.
Lesson Terms
- edge
- polygon
- quadrilateral
- vertex
Warm Up: Which One Doesn’t Belong: Bases and Heights
Problem 1
Which one doesn’t belong?
Triangle
Triangle
Triangle
Triangle
Activity 1: What Are Polygons?
Problem 1
Here are five polygons:
Here are six figures that are not polygons:
Select the figures that are polygons.
What do the figures you circled have in common? What characteristics helped you decide whether a figure was a polygon?
Activity 2: Quadrilateral Strategies
Problem 1
Find the area of two quadrilaterals of your choice. Show your reasoning.
Are you ready for more?
Problem 1
Here is a trapezoid.
Apply area-reasoning strategies—decomposing, rearranging, duplicating, etc.—on the trapezoid so that you have one or more shapes with areas that you already know how to find.
Use the shapes to help you write a formula for the area of a trapezoid. Show your reasoning.
Activity 3: Pinwheel
Problem 1
Find the area of the shaded region in square units. Show your reasoning.
Lesson Summary
A polygon is a two-dimensional figure composed of straight line segments.
Each end of a line segment connects to one other line segment. The point where two segments connect is a vertex. The plural of vertex is vertices.
The segments are called the edges or sides of the polygon. The sides never cross each other. There are always an equal number of vertices and sides.
Here is a polygon with 5 sides. The vertices are labeled
A polygon encloses a region. To find the area of a polygon is to find the area of the region inside it.
We can find the area of a polygon by decomposing the region inside it into triangles and rectangles.
The first two diagrams show the polygon decomposed into triangles and rectangles; the sum of their areas is the area of the polygon. The last diagram shows the polygon enclosed in a rectangle; subtracting the areas of the triangles from the area of the rectangle gives us the area of the polygon.