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Area of Polygons, Arc Length and Area Sectors

Printable Version for your convenience!

Title - Area of Polygons, Arc Length and Area Sectors
By - Gabriela Pena
Primary Subject - Math
Secondary Subjects - Computers & Internet, PE & Health
Grade Level - 10-12

Concept / Topic To Teach:
    Measurement
Texas Essential Knowledge and Skills Standards for Mathematics:
    111.34.b Geometry
      (G8) Congruence and the geometry of size. The student uses tools to determine measurements of geometric figures and extends measurement concepts to find perimeter, area, and volume in problem situations. The student is expected to:
        (A) find areas of regular polygons, circles, and composite figures;
        (B) find areas of sectors and arc lengths of circles using proportional reasoning
General Goal(s):
    The students will be able to demonstrate an understanding of the concepts and uses of measurements in composite figures and the arc length and area sector of a circle.
    • Find the area of the square cardboard
    • Find the area of the circle
    • Find the area of a sector and arc length
Specific Objectives:
  1. Given a cardboard cutout square, the students will have to decide the dimensions of the biggest circle that could be cut out from the square.
  2. Determine the difference between the area of the square and the circle.
  3. The students will then have to decide to divide the circle into 8, 10, or 12 sections.
  4. The students will find the arc length and area sector of a certain section.
Required Materials:
  • calculator
  • pencil
  • color pencils
  • markers
  • paper
  • formula chart
  • ruler
  • cardboard
  • scissors
  • camera
  • computer
  • Photo Story 3
Formulas:
  • Area of a Square = length x width [A=lw]
  • Area of a Circle = Pi x radius2 [A=(Pi)r2]
  • Circumference of a Circle = 2 x Pi x radius [C=2(Pi)r]
  • Area of a Sector = (measure of central angle/360) x area of circle) [A = (m/360)((Pi)r 2)]
  • Arc Length = (measure of central angle/360) x circumference [(m/360) x 2(Pi)r]
  • Pi = approximately 3.142
Anticipatory Set (Lead-In):
  • The teacher reviews how to find the areas of different polygons and properties of a circle.
  • The teacher models a summarization of the project through Photo Story 3.
Step-By-Step Procedures:
  1. Read about TEKS Objective 8 above
  2. Find the area of the cardboard square
    • Measure the length of the square
    • Use the formula for the area of a square
    • Find the square's area
  3. Find the area of the circle
    • Find the center of the circle
      • Find the midpoint of the lengths of the cardboard
      • Draw a plus sign by drawing a line connecting the opposite midpoints
      • Make a dot at the intersection of the lines, indicating the center of your circle
    • Find the radius by measuring it with a ruler
    • Draw the circle
    • Cut out the circle
    • Calculate the area of the circle
  4. Find the area of a sector and arc length
    • Find the area of the sector
      • Decide how many slices in the pizza and how many will be eaten
      • Draw the slices depending on how many degrees in each slice
      • Calculate the area of the sector they will eat
    • Find the arc length
      • Find the circumference of the circle
      • Find the arc length of the sector with the formula
  5. Summarize the project onto Photo Story 3 along with pictures.
Plan For Independent Practice:
  • Each group of four will have different responsibilities in the project.
    • The first person will explain how to find the area of the square and circle.
    • The second person will have to explain how many sections they decided on having and how many degrees each section is.
    • The third person will explain how to calculate the arc length.
    • The fourth person will explain how to calculate the area sector.
  • Everyone on the group will have to know how to do all the duties of the group because the teacher will decide which student plays what role.
  • Once the roles are assigned, a Photo Story 3 presentation is expected to summarize their project.
Closure (Reflect Anticipatory Set):
  • After the group presentations, the other groups will have a chance to ask question to have student interaction.
  • Then the teacher will join in targeting any area that has not been approached with open-ended questions.
Assessment Based On Objectives:
    Based on their presentation through Photo Story 3, the teacher determines if the objectives are mastered. If extra practice is needed, provide a four-question worksheet with similar problems.
Adaptations (For Students With Learning Disabilities):
  • The students will be put in groups with peers that are known to provide adequate assistance.
  • The teacher will assist the students in their target weakness areas.
  • If extra time is needed, then the teacher can have that student checkout a laptop with Photo Story 3 to work on it from home.
Extensions (For Gifted Students):
    GT students could do research to find out how many calories are in a slice of pizza and how that relates to determining area of sector.
Possible Connections To Other Subjects:
    When students find the area of a polygon or the volume of a shape, they can relate it when they are in health class to see what percents or proportions are in the amounts of calories.

E-Mail Gabriela Pena!