Areas of Kites and Related Figures Lesson 11.4

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Areas of Kites and Related FiguresLesson 11.4
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 ltBAD is a right angle
Find the area of the kite.
B
D

• A ½(10)(5) ½ (10)(12)
• 25 60
• 85 m2

C
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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.
B
D
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. ?BPX is a right triangle so BP 3 BY 6.
A ½ d1d2 A ½ (6)(8) A 24