Chapter 12 Measurement

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Chapter 12Measurement

• Section 12.2
• Measuring the Perimeter
• and Area of Polygons

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Perimeter

• The perimeter, P, of a polygon is the distance
  around the polygon or the sum of the lengths of
  each side of the polygon. Perimeter is a linear
  measurement.

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Common Formulas for Perimeter
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Area

• The area, A, of a polygon is the number of square
  units the polygon covers.

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A Question

• You have 100 to spend on fencing that costs
  2.50 per foot. What is the largest area you
  could fence in?

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Activity

• Relating Perimeter and Area
• (Rectangles and Squares)

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Investigation

• Draw a rectangle whose length is 6 cm and whose
  width is 4 cm.
• Draw a second rectangle whose length is 9 cm and
  whose width is 6 cm.
• What is the relationship between these two
  quadrilaterals?
• Find the perimeter and area of each.
• Compare the ratios between corresponding sides,
  perimeters, and areas. What do you notice?

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Comparing Perimeters and Areas of Similar Polygons

• The ratio of the perimeters is the same as the
  ratio of any two corresponding sides (scale
  factor).
• If the scale factor of two similar polygons is a
  b, then the ratio between their areas is a²
  b².

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Activity Connecting Area of Parallelograms,
Triangles, and Trapezoids

• On a piece of grid paper, draw a rectangle with a
  base of 6 cm and a height of 4cm. Find the area.
• What is the general formula for finding the area
  of a rectangle? Why?
• Use a colored pencil to rearrange the rectangle
  to make a parallelogram. Identify the base and
  height.
• How are the base and height related to the length
  and width of the rectangle? How are the areas
  related?

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Activity continued

• What would be the formula for finding the area of
  a parallelogram?
• Draw another parallelogram. Draw a diagonal of
  the parallelogram.
• What figures are formed? How are the areas of
  each related? What would be the formula for
  finding the area of a triangle?
• Draw a trapezoid. Draw a diagonal of the
  trapezoid.
• How can we develop a formula for finding the area
  of the trapezoid by using the area of the two
  triangles and the distributive property?

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Area Formulas
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Area Formulas
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Examples

• Textbook Page 691.
• 1.) 10
• 2.) 12
• 3.) 18
• 4.) 20

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Circumference of Circles

• The circumference, C, of a circle is the distance
  around the circle.
• How is circumference similar to perimeter?
• Different?

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Developing a Formula for Circumference

• Activity Discovering Pi
• Bring in several circular objects and have
  students use a piece of string and a ruler to
  determine the circumference and diameter of each
  circle. Then, they will determine the ratio
  between the circumference and the diameter, ? !

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Discovering Pi
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Circumference of a Circle Formula

• ? Circumference 3.14 or 22
• Diameter 7

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Developing Area Formula for a Circle

• Draw a circle and cut it into 8 equal parts.
• Arrange the parts into the general shape of a
  parallelogram.
• How can this be used to arrive at the area for a
  circle?

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Area of Circle Formula