1. a kite has two diagonals. we’ll label them. 2. the diagonals in a kite make a right angle. 3....
TRANSCRIPT
FIND THE AREA OF KITES, RHOMBUSES AND TRAPEZOIDS
AREA OF KITES – EXPLANATION
1. A kite has two diagonals. We’ll label them.
2. The diagonals in a kite make a right angle.3. Let’s put a rectangle around the kite because we know the formula for the area of a rectangle.4. The diagonals have the same lengths as the sides of the rectangle, so…5. Fill in the empty space around the kite with a different color.6. The kite takes up half the space of the entire rectangle, so…
Diagonal #1
Dia
gon
al #
2
90Dia
gon
al #
2
Diagonal #1
1
2
1
1 1
2
2 2
Area of a Kite = ½ (d1)(d2)
Area of the Rectangle = (d1)(d2)
Area = ½ (d1)(d2)
= ½ (9+35)(12+12)
= ½ (44)(24)= 528 square
units
FIND THE AREA OF THE KITE
37
12
15
15
37
35
9
12
Be sure to identify the diagonals right away.
FIND THE AREA OF THE KITE
Area = ½ (d1)(d2)
= ½ (6+15)(8+8)
= ½ (21)(16)= 168 square
units
17
610
10
17
610
17x
2 2 2
2
2
6 10
36 100
64
8
x
x
x
x
8 8
8
y
2 2 2
2
2
8 17
64 289
225
15
x
x
x
x
15
Be sure to identify the diagonals right away.
Use the Pythagorean Theorem to find the missing pieces of the diagonals
AREA OF RHOMBUSES – EXPLANATION
1. A Rhombus has two diagonals. Label them.
2. The diagonals make a right angle.3. Let’s put a rectangle around the
rhombus because we know the formula for the area of a rectangle.
4. The diagonals have the same lengths as the sides of the rhombus,
so…5. Fill in the empty space around the
rhombus with a different color.6. The rhombus takes up half the space
of the entire rectangle, so…
Diagonal #1Dia
gon
al #
2
90
Dia
gon
al #
2
Diagonal #1
1
2
1
1 1
2
2 2
Area of a Rhombus = ½ (d1)(d2)
Area of the Rectangle = (d1)(d2)
Special Note: …because a rhombus is a parallelogram, the formula for parallelograms will sometimes work as well.
FIND THE AREA OF THE RHOMBUS
60
10
10
10
10
Area = ½ (d1)(d2)
= ½ (5+5)( + )
= ½ (10)( )= square
units
Be sure to identify the diagonals right away.
Use the 30-60-90 triangle rules to find the missing pieces of the diagonals 6
0
30
10hypotenus
e
Long leg
Short leg
3
2
5
5 3 5 3
5 3
5
5
5 35 3
10 3
50 3
AREA OF A TRAPEZOID - EXPLANATION
1. A trapezoid has two bases and a height. Let’s label them.2. Let’s add a third horizontal line through the middle of the figure.3. Now let’s put a rectangle over the trapezoid.4. Finally, lets cut off the ends of the trapezoid and move them.5. This means the trapezoid and the rectangle have the same area. Area = (Avg of Bases) (Height)
Base 1
Base 2
Avg of Bases
Heig
ht
The Area of a Trapezoid =(Avg of Bases)
(Height)OR
½ (B1 + B2)(Height)
FIND THE AREA OF THE TRAPEZOID
Area=(Avg of Bases)(Height)
=½ (B1 + B2)(Height)
=½ (20 + 10)(8)
=½ (30)(8) = 120 square
units
10
8
20
Be sure to identify the bases and the height right away.
Base 1
Base 2
FIND THE AREA OF THE TRAPEZOID
Area=(Avg of Bases)(Height)
=½ (B1 + B2)(Height)
=½ (16 + 4)(Height)
=½ (20)(6) = 60 square
units
4
16Be sure to identify the bases and the height right away.
Base 1
Base 2
45
45
Use the 45-45-90 triangle rules to find the height
4
16 - 4 = 1212 / 2 = 6
6 6
6
Same
6We need to find a side on the triangle so we need to break Base 1 into three pieces.
h=6