Areas of Kites and Related Figures Lesson 11.3
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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. - PowerPoint PPT Presentation
Transcript of 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.
A kite = A△ABD + A△DBC
B
C
D
Two formulas
A
DB = 10m
BC = 13m
<BAD is a right angle
Find the area of the kite.
A = ½(10)(5) + ½ (10)(12)
= 25 + 60
= 85 m2
Theorem 105: The area of a kite equals half the product of its diagonals.
A kite = d1d2
2
1
A kite = ½ (10)(17)
= 85m2
B
C
D
A
DB = 10m
AC = 17m
Find the area of the kite.
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 = 4The 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
