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10.2 Area and Perimeter


Presents examples of nonstandard units of area which are followed by English and metric units of area, and develops formulas for areas of circles and familiar polygons through visual methods for determining area, perimeter, and circumference.

Subsections: Nonstandard Units of Area; Standard Units of Area; Perimeter; Areas of Polygons; Circumferences and Areas of Circles; Problem-Solving Application

One-page Math Activity: Areas of Pattern Blocks Using Different Units


The Investigation poses questions to generate interest in various mathematical topics from the text and encourages students to formulate and investigate their own conjectures. One use of the investigations is for term papers in which students report on their conjectures and the patterns they find.

Click on the Read Me file below to open the investigation in a Word file:
Read Me - Area Relationship Instructions (Word Format) (37.0K)

Click on Geometer's Sketchpad in the left menu for information
GSP file--Investigation 10.2: Area Relationships (13.0K)


Computer Investigation 10.2

Area Relationships*
  1. A kite (see figure) is a quadrilateral with two non overlapping pairs of adjacent sides that are congruent.

    2. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073022845/78543/LI_10_2a.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (17.0K)</a>

    a. There is an interesting relationship between the area of a kite and the product of its two diagonals. Experiment with some different kites and form a conjecture about this relationship.

    b. Does your conjecture hold for other quadrilaterals such as squares, rectangles, parallelograms, and trapezoids?

  2. A square has been constructed on each side of triangle T (see figure below). The shaded triangles have been formed by connecting the outer vertices of the squares.

    3. <a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073022845/78543/LI_10_2b.jpg','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (24.0K)</a>

    a. How are the areas of the 4 triangles related? Experiment with a few figures and form a conjecture.

    b. Test your conjecture by replacing triangle T by a right triangle or an obtuse triangle. Does your conjecture still to hold?

*This investigation may be carried out with software such as Cabri Geometry II, Geometer's Sketch Pad, or The Geometric Super Supposer.








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