Investigating Geometry: Surface Area and Volume

Henrico County Public Schools

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May 2006

Lesson 9-1: Area of 2-D Shapes


Heron's Formula: In a Δ let a, b, c be the sides, and let A be the area.
Heron's formula states -- heronformula.gif
The actual origin of this formula is somewhat obscure historically, and it may well have been known for centuries prior to Heron.

Objective:

The student will be able to determine the area of a variety of shapes including polygons, circles, and sectors of circles.

 Applet Directions Close 
    In the figure on the left, move points A, B, and C to solve the following:
  1. Find a triangle with perimeter 12 having integer area and integer sides.

  2. What different triangular regions could be formed by 10 meters of fencing?
    What would be the area of each? What questions could you ask about the shapes or the areas?.

  3. Find a triangle having integer sides and integer area that is not a right triangle. Can you find others? Generalize.

  Hands-On Activities Close 
  1. A farmer has four straight pieces of fencing: 1, 2, 3, and 4 yards in length. What is the maximum area he can enclose by connecting the pieces? Assume the land is flat.

  2. Sierpinski’s Triangle C.a.R.
  3. A Fresh Coat (pdf)
  4. Congruent Regions (pdf)

  Other Web Sites Close 
  1. Glencoe: On Line Quiz
  2. Area: Triangles, Squares, & Rhombi
    E-Z Geometry:
  3. Glencoe

  4. Area: Regular Polygons E-Z Geometry
  5. Glencoe

 Puzzles & Problems tangram Close 
  1. Explain the Missing Area C.a.R.
  2. Area of Regular Polygons