MEASUREMENT






Credits


Download this unit
(PDF version)

Student CopyTeacher CopyReference Copy

Activity 1 (Small-Group Activity)
Area and Perimeter
Measuring Shapes

Activity Summary

Students measure area and perimeter of various shapes. Use with Student Copy and Reference Copy.

Introduction

Make a unit square on a geoboard. Ask students what its perimeter and area are. Make several other figures on the geoboard and help students find the area of each. (Note that for very unusual figures, it is often easiest to find the area by making a rectangle around the figure, calculating the area of that rectangle, and then subtracting the areas of the pieces of the rectangle that the figure does not enclose. See example below.) Also ask about perimeters, although if you have any non-rectangular figures, you will have to use the Pythagorean Theorem or settle for estimated lengths of diagonal sides. Continue until students are comfortable at finding the area of figures that are made and are able to approximate the perimeter.

Figure 1
Objectives
  • To estimate, make, and use measurements to describe and compare phenomena.
  • To extend understanding of the concepts of perimeter and area.
  • To develop an appreciation of geometry as a means of describing the physical world.
  • To understand and apply geometric properties and relationships.
Answer Key

Area and Perimeter on a Geoboard

  1. The area is the length of one side multiplied by itself. The perimeter is 4 times the length of a side.
  2. There are many possible answers; one is a 4 x 1 rectangle with a unit square sitting on top of it.
  3. There are many possible answers; one is a square with sides 2 units long with a unit square attached.
  4. The area is 0.5 square units. The perimeter is 3.4 units.
  5. Another triangle with area 0.5 square units can easily be constructed by simply moving a vertex to the right or the left so that the base and height are still 1 unit.

New Carpets and Baseboards

The scaling on R2 for the shapes drawn is 1 inch represents 10 meters. Students' answers should be in meters.

Shape Area Perimeter
A 1 in2 is 100 m2 4 in is 40 m
B 0.5 in2 is 50 m2 3.41 in is 34.1 m
C 0.5 in2 is 50 m2 3.25 in is 32.5 m
D 0.25 in2 is 25 m2 2.62 in is 26.2 m
E 2.1875 in2 is 218.8 m2 6 in is 60 m
F 0.5 in2 is 50 m2 4.09 in is 40.9 m

Paper Bridge

Designs and maximum weight tolerances will vary from group to group. One very effective method of creating a bridge is to simply fold the paper accordion style.

Closing Discussion

[Have students cut out the figure in the Reference Copy that is like the one below.]

Figure 2

Find the area of this shape. The area is 63 square units. [Next, have students cut the shape out and also cut along the diagonal line to produce 4 pieces.] Make a square with these 4 pieces. What would you say that the area is? The area of the 8 x 8 square-like figure will appear to be 64. Next, make a rectangle from the 4 pieces. What would you say that the area is now? The area of the 5 x 13 rectangular-like figure will appear to be 65. Is it possible for the area to keep changing like this? Why does the area appear to be changing? Of course, it is not possible for the area to keep changing. The illusion is due to the fact that the shapes that are along cut edges on the interior of the larger square and rectangle look like squares but are not really squares.


© Copyright
Area 10 Mathematics and Technology Professional Development Center
Permission is granted to duplicate these materials for classroom use.

Last updated on 1/30/1999
Comments: egalindo@indiana.edu
http://www.indiana.edu/~atmat/units/measurement/mea_t2.htm