Areas of Trapezoids, Rhombuses, and Kites

1
Section 7-4

• Areas of Trapezoids, Rhombuses, and Kites

2
Theorem 7-10Area of a Trapezoid

• The area of a trapezoid is half the product of
  the height and the sum of the bases
• A½h(base1 base2)

Base1
h
Base2
3
Example Find the Area
21 in
16 in
38 in
A ½ (b1 b2)(h)
A ½ (21 38)(16)
A (29.5 in)(16 in)
A 472 in²
4
Find the area of the Trapezoid
Area 144 sq. units
5
Find Area using triangle rules
M
11
X 8/2 4
8 ft
Y
4v3
60?
M 15 4 11
X
4
Y 4v3
15 ft
A ½ (11 15)(4v3)
A 52v3 ft²
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What do we know about Rhombuses???

• Sides are congruent

Diagonals bisect each other
Sides are congruent
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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.
• A½(diagonal1 diagonal2)

Diagonal 1
Diagonal 2
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Find Area of Rhombus
A ½ (d1)(d2)
9 m
12 m
A ½ (18 m)( 24 m)
A 216 m²
9
Find the Area
We need to find the length of the other diagonal
B
15 m
9m
BEC is a Right Triangle
C
E
A
12 m
Using the Pythagorean triple, BE 9 m
D
Or using Pythagorean Theorem a² b² c²
A ½ (d1)(d2)
A ½ (18 m)(24 m) 216 m²
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What do we know about Kites??

• Diagonals are perpendicular to each other

Each diagonal forms the base of an isosceles
triangle
The one diagonal bisects the angle to create two
congruent angles where we might be able to use
the special triangle rules
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Homework

• Page 376
• 2-28 e