Transcript Chapter 7 Lesson 4 - Mrs.Lemons Geometry
Chapter 7 Lesson 4
Objective: To find the areas of rhombuses and kites.
Theorem 7-11
: Area of a Rhombus or a Kite The area of a rhombus or a kite is half the product of the lengths of its diagonals.
A
1 2
d
1
d
2
d 2 d 1 Rhombuses and kites have perpendicular diagonals.
Example 1:
Finding the Area of a Kite
Find the area of kite KLMN. KM=2+5=7 LN=3+3=6
A A
1 2 2 1
d
1
d
2 ( 7 )( 6 )
A
1 2 ( 42 )
A
21
m
2 L K 2m 3m 3m N 5m M
Example 2:
Finding the Area of a Kite
Find the area of kite KLMN. KM=1+4=5 LN=3+3=6
A A
1 2 2 1
d
1
d
2 ( 5 )( 6 )
A
1 2 ( 30 )
A
15
m
2 L K 1m 3m 3m N 4m M
Example 3:
Finding the Area of a Kite
Find the area of kite with diagonals that are 12 in. and 9 in. long.
A A
1 2 2 1
d
1
d
2 ( 12 )( 9 )
A
1 2 ( 108 )
A
54
m
2
The diagonals of a rhombus bisect each other.
Example 4:
Finding the Area of a Rhombus
B 15m Find the area of rhombus ABCD.
∆BEC is a right triangle. Use the Pythagorean Theorem to find BE.
A E 12m
a
12 2 2 144
b
2
b b
2 2
b
2 81
c
2 15 2 225
b
2
b
9 81
AC
=12+12=
24 BD
=9+9=
18
A A A
1 2 1 2 2 ( 18 )( 24 ) ( 2 432 )
A
216m 2 D C
Example 5:
Finding the Area of a Rhombus
B Find the area of rhombus ABCD.
∆BEC is a right triangle. Use the Pythagorean Theorem to find BE.
a
12 2 2 144
b
2
b b b
2 2 2 25
c
2 13 2 169
b b
2 5 25
AC
=12+12=
24 BD
=5+5=
10
A A A
1 2 1 2 2 ( 10 )( 24 ) ( 2 240 )
A
A 120m 2 24m 12m E D 12m 13m C