Midpoint of Polygons

Lesson 3: Midpoint - Polygons

   Constructing Knowledge

There are times where it is necessary to find the middle of an object. For instance, if you want to be sure that a chocolate bar is cut exactly in half, you can find the midpoint of its length and cut the bar at that point. This method of measuring will work for 2D shapes.

As a general rule, to find the midpoint of any shape:

1. Find the midpoint of each side.
2. Connect the midpoint of one side to the midpoint of the opposite side, for shapes that have an even number of sides, or connect the midpoint of a side to the opposite vertex for shapes with an odd number of sides. The midpoint of the object is where the lines intersect.

   Multimedia

A video describing finding the midpoint of a rectangle is provided.

EXAMPLE 1

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Find the midpoint of the rectangle using a ruler and pencil.

Solution

Step 1: Find the midpoint of each side.

Midpoint of length = 12 ÷ 2
= 6 inches

Midpoint of width = 7 ÷ 2
= 3.5 inches



Step 2: Connect opposing midpoints with a line, using a ruler.



The midpoint of the rectangle is where the two lines intersect.

   Constructing Knowledge

A shortcut for finding the midpoint of any rectangle or square is to connect opposite corners (vertices) with diagonal lines. The midpoint of the rectangle is where the two lines intersect.

EXAMPLE 2

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Find the midpoint of the square.

Solution

Draw diagonals connecting opposite corners (vertices).



The midpoint is where the two diagonals intersect.




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