- 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.MultipleIntelligences
- Be sure to teach the material in this lesson in an interactive way. I would recommend going through the
material without the text first. That way each student can explore the different characteristics of the three
figures without using the information in the text as a guide. - Then go back to the text and go over the information in it. The students will see this in a new way because
they will have already “discovered” it. - Here are some notes on each figure in the section. This will help the students to “break down” the content.
- Trapezoid- quadrilateral with one pair of parallel sides.
- Formula-^12 (b 1 +b 2 )h
- Finding the Area of a Rhombus
- Frame a rhombus in a rectangle.
- Notice all of the triangles.
- 4 triangles to fill in the rhombus
- 8 triangles fill in the rectangle.
- 4 is half of 8
- Area of rhombus=^12 area of a rectangle.
- Formula=A=^12 d 1 d 2
- Finding the Area of a Kite
- Frame in a rectangle.
- Notice the similarities with the rhombus.
- Use the same formula as a rhombus.
- Intelligences- linguistic, logical- mathematical, visual- spatial, interpersonal.
III.SpecialNeeds/Modifications
- Review finding the area of a rectangle.
- Review finding the area of a parallelogram.
- Review finding the area of a triangle.
- Show how more than one figure can be combined together to create a new figure.
- Example- a rectangle and a triangle together.
- Review finding the area of such a figure.
IV.AlternativeAssessment
- Observe students as they work through the explorations.
- Allow a lot of time for students to speculate and share their findings.
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.
4.10. Perimeter and Area