 EMAT 6700

by Brad Simmons

Perimeter and Area of Irregular Shapes

Use geometer's sketchpad to find the perimeter and area of Irregular Shapes.

Problem:  Find the perimeter and area of the figure below. It would be extremely useful to know the perimeter of a rectangle is twice its length plus twice its width.

P = 2L + 2W

Furthermore, the area of a rectangle is equal to the length times the width.

A = LW

Solution using geometer's sketchpad:

Divide the irregular shaped figure above into rectangles.  This can be done in many different ways. The figure below divides the irregular shape into two rectangles. The two rectangles are rectangle ABFD and rectangle FCEG.

How many other ways can this irregular shape be divided into rectangles?

Can it be divided into more than two rectangles?

For a Geometer's Sketchpad sketch of this figure that can be manipulated please click here.

To find to the area of the irregular figure, first find the areas of rectangle ABFD and rectangle FCEG.

1. Select the four corner point of the rectangle.

2. Construct quadrilateral interior.

3. Select quadrilateral interior and measure area. The area of the irregular shape is the area of the two rectangles added together.

Use the measure calculate feature of Geometer's Sketchpad to add the areas. The perimeter of the irregular shape is equal to the sum of the six segment around the outside of the figure.

1. Select the endpoints of the segment to be measured.

2. Measure distance.

3. Use the measure calculate feature of Geometer's Sketchpad to add the distances. Find the Perimeter and Area of each Irregular Shape

1. Click here for a sketch that can be manipulated. 2.  Click here for a sketch that can be manipulated. 3Click here for a sketch that can be manipulated. Return