Lesson 11: Polygons

Let’s investigate polygons and their areas.

11.1: Which One Doesn’t Belong: Bases and Heights

Which one doesn't belong?

Four triangles on a grid, labeled S, T, U, and V.

11.2: What Are Polygons?

Here are five polygons:


Here are six figures that are not polygons:

  1. Circle the figures that are polygons.

    Ten figures labeled A--J.
  2. What do the figures you circled have in common? What characteristics helped you decide whether a figure was a polygon?

11.3: Quadrilateral Strategies

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

Six quadrilaterals labeled A--F.

11.4: Pinwheel

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

A shaded polygon on a grid.


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 $A, B, C, D$, and $E$.

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.

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. 

Practice Problems ▶




A quadrilateral is a four-sided polygon.

vertex (vertices)

vertex (vertices)

A vertex is a point where two edges meet in a polygon or a polyhedron.



A line segment in a polygon is called an edge (it is also called a side). A line segment where two faces meet in a polyhedron is also called an edge.



A line segment in a polygon is called a side (it is also called an edge).

Sometimes the faces of a polyhedron are called its sides.



A polygon is a two-dimensional figure composed of a sequence of straight line segments, connected end-to-end, with the last one connecting back to the first. We call the line segments the edges or sides of the polygon. We call a point where the edges connect a vertex. The edges of a polygon never cross each other.

The plural of vertex is vertices. A polygon always encloses a two-dimensional region.

Here is a polygon with five vertices $A$, $B$, $C$, $D$, and $E$ and five edges (or sides): $\overline{AB}$, $\overline{BC}$, $\overline{CD}$, $\overline{DE}$, and $\overline{EA}$.