Trapezoids, Rhombi and Kites
I.SectionObjectives
- Understand the relationships between the areas of two categories of quadrilaterals: basic quadrilaterals and
special quadrilaterals. - Derive area formulas for trapezoids, rhombi and kites.
- Apply the area formula for these special quadrilaterals.
II.Cross-curricular-RoomDesign
- Tell students that they are going to design a room that has a trapezoidal shape.
- Students can complete this in connection with the Technology Integration if you choose.
- If not, have the students use the dimensions of their own bedroom (they did this in the last lesson), or the
classroom or a standard size bedroom( 11 × 10 )for example. - Students are going to redesign this area as a trapezoid.
- They want to come as close to the original area as possible.
- So if the room was 11×10, the area is 110 sq feet.
- How can you come close to the same area if the shape of the room is a trapezoid?
- Students should draw their design on grid paper and explain their thinking.
- Allow time for students to share their work when finished.
III.TechnologyIntegration
- This is a website that shows a house designed as a trapezoid.
- http://www.momoy.com/2009/04/02/l-house-beautiful-trapezoid-house-design-by-philippe-steubi-architekten-gmbh/
- Students can look at the trapezoid shape of the house and the floor plan is also included.
- There are views of the inside of the house and the outside of the house as well as some of the rooms.
- Conduct a discussion about the house. What would be the challenges of designing and building such a house?
IV.NotesonAssessment
- Assessment will come with student presentations and work product.
- What did students learn about the relationship between rectangles and trapezoids?
- Were they able to come up with a room with an area close to the original?
- Who got the closest?
- Provide students with feedback on their work.
Area of Similar Polygons
I.SectionObjectives
- Understand the relationship between the scale factor of similar polygons and their areas.
- Apply scale factors to solve problems about areas of similar polygons.
- Use scale models or scale drawings.
II.Cross-curricular-NationalMallMapping
3.10. Perimeter and Area