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Activity 2 (Small-Group Activity)
Area and Perimeter
Measuring Shapes


  • geoboard and rubber bands
  • calculator
  • ruler (English)
  • 3 sheets of 22 cm x 28 cm paper (regular notebook paper)
  • scissors
  • glue or tape
  • centicubes or other unit of mass
  • Reference Sheet

Area and Perimeter on a Geoboard

  1. On your geoboard, the horizontal (or vertical) distance between any two adjacent pegs is 1. Make three different squares of any size. For each, record the length of one side, the area and the perimeter.
  2. Find a shape with an area of 5 square units and with a perimeter of 12 units. Draw the shape.
  3. Find a shape with an area of 5 square units and with a perimeter of 10 units. Draw the shape.
  4. On your geoboard, make a triangle that is half the size of a unit square. What is its area? Now, use the Pythagorean Theorem and your calculator to find the perimeter (round your answer to the nearest tenth).
  5. Now, find another triangle with an area of 1/2 square units. Draw the shape and record its perimeter.

New Carpets and Baseboards

You may have seen floor plans or other objects that are drawn to scale. In many occupations, a large object must be pictured in proportion to its actual shape and size. The Reference Sheet has scale drawings of several shapes. Suppose these shapes are really drawings of floors that are to be carpeted and new baseboards are to be installed.

You see a scale (the line labeled 10 m) on the Reference Sheet that represents 10 meters. Use this scale to find measurements of the shapes and then to complete the table below. You may use a ruler. For each shape, find the area to be carpeted and the perimeter measurement for new baseboards. Round final answers to the nearest tenth of a meter.

Shape Area Perimeter
A . .
B . .
C . .
D . .
E . .
F . .

A Paper Bridge

You may have noticed that construction materials come in a variety of sizes and shapes.

Your task is to construct three bridge designs from regular notebook-sized paper and to see which design is the sturdiest. Build a structure from each sheet of paper that is at least 5 cm wide and spans the 15 cm between tables.

After creating a bridge design, determine how much weight it will hold as follows

  1. Place two flat tables 15 cm apart.
  2. Place the design between the 15 cm space made with the desks.
  3. Gently, put one unit mass at a time in the center of the structure.
  4. The number of units the structure holds before buckling is its maximum loading.

Record your results in a table like the one below.

Design Cross-Sectional Sketch Maximum Loading (grams)
#1 . .
#2 . .
#3 . .

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

Last updated on 1/30/1999