Chapter 7 Lesson 4Chapter 7 Lesson 4

Objective:Objective: To find the areas of rhombuses and kites.

Theorem 7-11Theorem 7-11: : Area of a Rhombus or a KiteArea of a Rhombus or a KiteThe area of a rhombus or a kite is half the The area of a rhombus or a kite is half the product of the lengths of its diagonals.product of the lengths of its diagonals.

d2

d1

212

1ddA

Rhombuses and kites have perpendicular Rhombuses and kites have perpendicular diagonals.diagonals.

Example 1:Example 1:Finding the Area of a KiteFinding the Area of a Kite

Find the area of kite KLMN.

2m5m

3m

3m

KK

LL

MM

NN

KM=2+5=7LN=3+3=6

212

1ddA

)6)(7(2

1A

)42(2

1A

221mA

Example 2:Example 2:Finding the Area of a KiteFinding the Area of a Kite

Find the area of kite KLMN.

1m4m

3m

3m

KK

LL

MM

NN

KM=1+4=5LN=3+3=6

212

1ddA

)6)(5(2

1A

)30(2

1A

215mA

Example 3:Example 3:Finding the Area of a KiteFinding the Area of a Kite

Find the area of kite with diagonals that are 12 in. and 9 in. long.

212

1ddA

)9)(12(2

1A

)108(2

1A

254mA

Example 4:Example 4:Finding the Area of a RhombusFinding the Area of a Rhombus

Find the area of rhombus ABCD. 15m

12mAA

BB

CC

DD

2121

ddA

)24)(18(21

A

)432(21

A

2216mA

∆∆BEC is a right triangle. BEC is a right triangle. Use the Pythagorean Use the Pythagorean Theorem to find BE.Theorem to find BE.

EE

222 cba 222 1512 b

225144 2 b812 b

812 b9b

The diagonals of a rhombus bisect each other.The diagonals of a rhombus bisect each other.

AC=12+12=2424BDBD=9+9=1818

Example 5:Example 5:Finding the Area of a RhombusFinding the Area of a Rhombus

Find the area of rhombus ABCD. 13m

24mAA

BB

CC

DD

2121

ddA

)24)(10(21

A

)240(21

A

2120mA

∆∆BEC is a right triangle. BEC is a right triangle. Use the Pythagorean Use the Pythagorean Theorem to find BE.Theorem to find BE.

222 cba 222 1312 b

169144 2 b252 b

252 b5b

AC=12+12=2424BDBD=5+5=1010

12m 12m

EE

AssignmentAssignment

pg. 376 - 378 pg. 376 - 378 #14-20;29-31;35-#14-20;29-31;35-

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