How to Find the Area of Regular Polygons

Finding the area of regular polygons is the topic of this geometry math video.

First, the video discusses the parts of a regular polygon: apothem and radius. The center of the polygon is the same as the center of the circumscribed circle. The radius of the polygon is the distance from the center of the polygon to its vertex. The number of radii is determined by the number of sides. The apothem it the perpendicular distance from the center of the polygon to a side.

The first example models how to find the different angles of a regular polygon formed by the radius and the apothem. First, you divide the number in interior angles into 360 degrees. Once you have that you can figure out the other two angles quite easily.

Before applying the the area formula of a regular polygon, the video reviews the formula:

A = \frac{1}{2}ap

It is good to note that a = length of the apothem and p = perimeter of the polygon. The perimeter may not be calculated. In that case you multiply the number of sides by the length of each side.

This example is similar to the video, but it is different:

What is the area of a polygon with sixteen 36 in. sides and an apothem of 18\sqrt{3} in.

A = \frac{1}{2}ap

A = \frac{1}{2}(18 \sqrt{3}(16*36))

A = 5184 \sqrt{3} in^2 \approx 8979.0 in^2

Questions for the comment section:

Comparing example 2T on the video and the problem above, how are the problems alike? How are the problems the same?

Example 3T is finding the area of a regular polygon, but you need to find the length of the apothem using the 30-60-90 triangle relationship.

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Area of a Triangle – Hands on Tactile Activity

I have been making videos to use in class, so the blog is going to be videos of me teaching. If you have related questions, post your questions in the comment section. I will do my best to answer you in a timely manner. This geometry video math lesson develops the area of a triangle from the area of a parallelogram. Grid or graph paper,  a pencil and a straight edge will be necessary if you want to complete the task yourself. If you want to really make the connection between the heights of the parallelogram and the triangle, you should create your own triangle with a different base and height. To use this as a hands on tactile geometry lesson, download grid paper here.

The connection is made through the heights of the the objects. The height of the parallelogram is one half the height of the triangle. To use this as a hands on tactile geometry lesson, download grid paper here.

Area of a Parallelogram Hands On Activity

This lesson focuses on the development of the area formula for a parallelogram. The development and activity is tactile or hands on in manner. To fully participate, download grid paper here.

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