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Areas of Kites and Related Figures Lesson 11.3

Areas of Kites and Related Figures Lesson 11.3. Work as a team to solve the following problem: In rectangle ABCD, X and Y are mid-points of AB and CD and PD  QC. Compare the area of quadrilateral XQYP with the area of ABCD. Prove your conjecture. Two formulas.

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Areas of Kites and Related Figures Lesson 11.3

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  1. Areas of Kites and Related FiguresLesson 11.3

  2. Work as a team to solve the following problem: In rectangle ABCD, X and Y are mid-points of AB and CD and PD  QC. Compare the area of quadrilateral XQYP with the area of ABCD. Prove your conjecture.

  3. Two formulas A kite = A△ABD + A△DBC A DB = 10m BC = 13m <BAD is a right angle Find the area of the kite. D B • A = ½(10)(5) + ½ (10)(12) • = 25 + 60 • = 85 m2 C

  4. Theorem 105: The area of a kite equals half the product of its diagonals. A kite = d1d2 A DB = 10m AC = 17m Find the area of the kite. D B A kite = ½(10)(17) = 85m2 C

  5. Find the area of a rhombus whose perimeter is 20 and whose longer diagonal is 8. A rhombus is a parallelogram, so its diagonals bisect each other. It is also a kite, so its diagonals are perpendicular to each other. XZ = 8 & XP = 4 The perimeter is 20 so XB = 5. ΔBPX is a right triangle so BP = 3 & BY = 6. A = ½ d1d2 A = ½ (6)(8) A = 24

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