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Area of a Kite and Rhombus
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Printed: July 21, 2012
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CONCEPT 1 Area of a Kite and Rhombus
Lesson Plan
Launch (5 min)
• Students mark-up the kite and rhombus diagrams with congruency markings for their side and diagonals toactivate prior knowledge.
• The one thing the two have in common is perpendicular diagonals.
Presentation (20 min)
• Investigation: Area of a rhombus & kite
– Label & highlight d1 and d2 on the paper models– Task 1: Find the area in as many ways as possible. Explain how you did so and be prepared to present.– Task 2: Find the perimeter.– Area of a rhombus or kite = 1
2 b1∗b2– Expect to see students cutting and rearranging the rhombus and kite to find the area in the following
ways:
* form a rectangle (most often)* calculate the sum of four triangle areas (slightly less often than the rectangle)* form a parallelogram (least often)
– Try to have a student present each solution method everyone gains from the diversity of methods.Students record their findings and any additional notes in the space provided at the bottom of the firstpage.
• Practice Together: lead a think aloud with students taking notes.
Practice (25 min)
• Students choose 5 of the practice problems. Emphasize finding your ‘find’ (that which you’re looking for) andcircling it and also using the formula or area finding method developed earlier.
Conclusion (10 min)
• Write a letter explaining the process of finding a missing diagonal.
Exit Ticket (5 min)
Materials
Pre-cut kites and rhombi, leaving them on their graph paper
Scissors (in case students want to cut up the figures and move pieces around)
Concept 1. Area of a Kite and Rhombus
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Launch
1. Mark-up the rhombus and the kite below with everything you know about their sides and diagonals .
2. Name one thing the two quadrilaterals have in common.
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Investigation
Investigation : Rhombus and Kite Area
Experiment by sketching, cutting, marking up, etc. the rhombus and kite you receive. Record below every way youfind their areas. Using d1 and d2 for diagonals, write a formula for each. Be ready to present your findings. Bonus:find their perimeters!
Practice Together: Find the area and perimeter of each polygon. Show your work.
1. Given: the figure is a rhombus.
Concept 1. Area of a Kite and Rhombus
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2. Given. The figure is a kite.
Practice
Practice: Choose at least 5 exercises to do from the menu below. SHOW ALL WORK
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Conclusion
Given: The area of a rhombus is 60 cm squared. One diagonal is 12 cm.
Find: The length of the other diagonal.
Write a letter explaining to a student who has been absent how to use the area formula for a rhombus to find thelength of the other diagonal.
Concept 1. Area of a Kite and Rhombus
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Homework
CIRCLE what you are finding. WRITE the formula and ANNOTATE your diagram with congruencies.
1. Find the area.
2. Find the area.
3. Describe the error in the work below. How should the problem have been done? Explain.
A =(21)(12)
2A = (21)(6)
A = 126m2
4. Find the area and perimeter of the rhombus.
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5. A rhombus has an area of 60 square centimeters. If the length of one diagonal is 12 cm, find the length of theother.
Exit Ticket
Concept 1. Area of a Kite and Rhombus
