Finding the Area of Irregular Figures

In this lesson plan from Illuminations students will estimate the area of irregular shapes, decompose irregular polygons into simple polygons, and determine the area of an irregular polygon by summing the area of its composite shapes. Students will have the opportunity to draw freeform irregular shapes, compose irregular shapes from standard polygons, and actively calculate area of an irregularly shaped classroom. This lesson gives the kinesthetic learner the opportunity to use his/her hands and move around the room.

Weblink address (URL): 
Finding the Area of Irregular Figures

Standards & Objectives

Learning objectives: 

Learning Objectives

Students will:

  • Estimate the area of irregular shapes.
  • Decompose irregular polygons into squares, rectangles, triangles, and other familiar shapes.
  • Determine the area of an irregular polygon by summing the areas of its composite shapes.

Lesson Variations

Blooms taxonomy level: 
Understanding
Extension suggestions: 

Extensions:

  • When creating floor plans of the room in the school building, have students draw them to scale. Students could draw their plans on centimeter grid paper, for instance. They could include desks, shelves, and other items found in the rooms in their scale drawings.
  • Have students create nets for prisms and pyramids. Ask students to find the surface area of these shapes using the method of decomposition.
  • Have students determine the area of a shape that is drawn within a rectangle, such as the pentagon contained in the rectangle below.
  • In order to determine the area of the pentagon, students will have to subtract the area of the triangles from the area of the rectangle. [The area is 17.5 square units.]

 

 

Helpful Hints

Materials:

  • Rulers, yardsticks, meter sticks, or measuring tapes Calculators
  • Scissors
  • Polygons Activity Sheet 
  • Centimeter grid paper (optional)
  • Floor plan of a room in your school (optional)
  • Computers or tablets with internet access (optional)

References

Contributors: 
Ashley King
Originator: 
Ayers Institute for Learning & Innovation