11.4 Areas of Kites and Related Figures

A kite = A △ABD + A △ DBC

B

C

D

Two formulas

ADB = 10m

AE = 5 m

EC = 12 m

BC = 13m

<BAD is a right angle

Find the area of the kite.

E

Use correct formula

A kite = A ABD + A DBC△ △

= ½ (BD)(AE) + ½(BD)(EC)

= ½(10)(5) + ½ (10)(12)

= 25 + 60

= 85 m2

T105: The area of a kite equals half the product of its diagonals.

A kite = d1d22

1

A kite = ½ (10)(17)

= 85m2

Find the area of a kite with diagonals 9 and 14

Draw, label, write all steps.

Find the area of a rhombus whose perimeter is 20 and whose longer diagonal is 8.

What do you know about the inside triangles?

5

5

4

3

Remember: a rhombus is a parallelogram so the diagonals bisect each other. It is also a kite, so its diagonals are perpendicular to each other.