Activity 11.2: Area and perimeter

  • Due May 25, 2022 by 11:59pm
  • Points 30
  • Submitting a text entry box or a file upload

Math Activity: Area and Perimeter of Polygons

Purpose: Explore areas of polygons

Materials: A Geoboard or Geoboard app Links to an external site., and graph paper or Download dot paper

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Note: When using a Geoboard, we only use the points as vertices. Distances between points, vertically and horizontally is assumed to be 1 unit.

Help: Tutorial Video, part 1 Links to an external site., Download Notes

Directions:

We define area to be base x height of a rectangular region. Area is measured in unit squares, or square units. Since a right triangle is always half of some rectangle, then the area of a right triangle is base x height ÷ 2.

We will use these facts about area basics to find areas of other polygons.

triangle b=2, h=3, rectangle composition

The yellow triangle above lives within this 3x4 rectangle. This rectangle makes a composition around the triangle; a decomposition would cut up the triangle internally. If we strip away the triangles in the upper left (4x3÷2 =6) of the rectangle and the lower right (2x3÷2 = 3) of the rectangle, then we are left with 12 - 6 - 3 = 3 square units for the yellow triangle. What is a base and height of the yellow triangle?

  1. Triangle Areas:
    Find the areas of the triangles by using the basic area facts from above. Show your compositions/decompositions on paper.
    1. triangle 2x3 right angle left side
    2. triangle b=2, h=3, isosceles
    3. triangle 2x3 right angle right side
    4. triangle b=2, h=3, skewed right a little
    5. triangle b=2, h=3, skewed right
       
  2. More Triangle Areas
    On a Geoboard (or dot paper or graph paper), make three different triangles each with areas 3.5 square units. Remember, vertices of the triangles must be on points.
  3. Parallelogram Areas
    parallelogram to rectangle
    A parallelogram can be transformed into a rectangle by cutting and pasting.
    On a Geoboard (or dot paper or graph paper), make 3 different parallelograms and show how to find their areas by cutting and pasting into rectangles.
  4. Trapezoid Areas
    trapezoid composition bounding rectangle trapezoid decomposition triangles and rectangles
    We can find the area of a trapezoid through either decomposition or composition with rectangles and right triangles.
    On a Geoboard (or dot paper or graph paper), make 3 different trapezoids and show how to find their areas.

  5. State the area formulas for :
    1. Triangle: 
    2. Parallelogram: 
    3. Trapezoid:

  6. Find the perimeter of one of each of your polygons from parts 2, 3, and 4:
    1. Triangle: 
    2. Parallelogram: 
    3. Trapezoid:

 

1653548340 05/25/2022 11:59pm