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Exploring Composition and Decomposition of Shapes: Area Formulas for Trapezoids, Rhombuses, and Kites

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In this activity, students will dive into the concepts of composition and decomposition to derive area formulas for trapezoids, rhombuses, and kites. We’ll begin by analyzing patterns in the number of stripes on male and female punky fish to introduce problem-solving through ratios. Following this, we will review key properties of these geometric shapes and engage in exercises to calculate their areas. By the end of the lesson, students will have a better understanding of how to apply mathematical concepts to real-world shapes.

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Exploring Composition and Decomposition of Shapes: Area Formulas for Trapezoids, Rhombuses, and Kites

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  1. Bellwork Solve for x 14

  2. Composition/Decomposition Activity Section 11.2

  3. Bellwork 2xo A male punky fish has 9 stripes, while a female punky fish has 8 stripes. If the number of stripes on all the punky fish in a tank totals 86, what is the ratio of male fish to female fish? Two triangles of equal area have congruent sides as shown. Determine the degree measure of x, the smaller of the two vertex angles. xo 14

  4. Areas of Trapezoids, Rhombuses and Kites Section 11.2

  5. The Concept • Yesterday we completed a worksheet that discussed the idea of composition and decomposition of objects in order to find area • Today we’re going to look at how we can use this to develop and area formulas for each of the three objects

  6. Review of shapes Parallelogram h b Triangle h b

  7. Trapezoids, Kites & Rhombuses, oh my! Let’s review these objects… • Trapezoid • Quadrilateral in which only two sides are parallel • Rhombus • Equilateral parallelogram • Kite • Quadrilateral with two pair of adjacent congruent sides

  8. Trapezoid b1 h b2

  9. Trapezoid Example Find the area of the object below 5 8 15

  10. Trapezoid Example Find the area of the object below 10 12 12 22

  11. Rhombus d2 d1

  12. Rhombus example Find the area of the object below 15 24

  13. Rhombus example Find the area of the object below 10 10 60o

  14. Kite d2 d1

  15. Kite Example Find the area of the object below 23.5 51

  16. Kite Example Find the area of the object below 20

  17. Homework 11.2 Exercises 10, 12, 15, 16-18, 24-29

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