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6-8 Grade 6 Unit 1 Lesson 11

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IM K-5 Math
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Lesson 11

11.1 Warm-up 11.2 Activity 11.3 Activity 11.4 Activity Student Lesson Summary Glossary

Unit 1, Lesson 11

Polygons

Grade 6

11.1

Warm-up

Which three go together? Why do they go together?

11.2

Activity

These five figures are polygons.

<p>5 polygons</p>

The next six figures are not polygons.

<p> six figures that are <em>not</em> polygons:</p>

Circle 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?

11.3

Activity

Standards Alignment

Building On

Addressing

6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard

Building Toward

Find the area of two quadrilaterals of your choice. Show your reasoning.

Six quadrilaterals on a grid labeled A--F.

11.4

Activity

Standards Alignment

Building On

Addressing

6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard

Building Toward

Find the area of the shaded region in square units. Show your reasoning.

A shaded polygon on a grid.

Student 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 , and .

A polygon encloses a region. The area of a polygon is the area of the region inside it.

Polygon with 5 sides

We can find the area of a polygon by decomposing the region inside it into triangles and rectangles.

Three identical five-sided polygons. The first two are divided up into triangles in rectangles. The third is surrounded by a rectangle, the area of which outside the polygon is shaded.

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 with a rectangle. Subtracting the areas of the triangles from the area of the rectangle gives us the area of the polygon.

A polygon is a closed, two-dimensional shape with straight sides that do not cross each other.

Figure is an example of a polygon.

Polygon with 5 sides

Standards Alignment

Building On

4.G.2

Classify two-dimensional figures based on the presence or absence of parallel or perpendicular lines, or the presence or absence of angles of a specified size. Recognize right triangles as a category, and identify right triangles. (Two-dimensional shapes should include special triangles, e.g., equilateral, isosceles, scalene, and special quadrilaterals, e.g., rhombus, square, rectangle, parallelogram, trapezoid.)

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Addressing

Building Toward

Standards Alignment

Building On

Addressing

Building Toward

6.G.1

Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

View Full Standard