In this activity, students find the area of regular polygons using a summation approach and compare the summations with area calculated by Cabri Geometry Application. They also examine patterns of finding area and perimeter as the number of sides of the polygon is changed.

Before the Activity

See the attached PDF file for detailed instructions for this activity

Print pages 59 - 66 from the attached PDF file for your class

During the Activity

Distribute the pages to the class.

Follow the Activity procedures:

Construct a line segment

Construct a circle with the line segment as radius

Draw a regular pentagon within the circle

Construct a triangle using the segment as one of the sides and two additional segments

Find the midpoint (m) of the base of the triangle

Construct an altitude of the triangle (apothem of the regular polygon)

Measure and record length of base, height, and radius of polygon

Calculate and record the area of the triangle using the formula 1/2 base length (B) x height (H)

Observe that the polygon can be further divided into congruent triangles like the first one

Find the number of triangles that can be constructed in the pentagon

Note that the internal area of the polygon, can be calculated by the formula 1/2 (B/H) x n, where n is the number of triangles inside the polygon

Find the perimeter of the pentagon and then calculate the area of a pentagon using the formula: Area of polygon is = 1/2 (perimeter) x apothem

Use the Voyage 200 PLT to directly calculate the area of the pentagon and compare the three methods

Construct other polygons and find their area and perimeter and enter the values in a table

Observe as the number of sides of the polygon increases, the geometric shape approaches a circle

The perimeter of a circle is given by the formula 2 π r and area is given by the formula π r^{2}

Compare the area of a circle with a polygon with many sides

After the Activity

Review student results:

As a class, discuss questions that appeared to be more challenging