Areas of parallelograms, triangles, kites, trapezoids and rhombi.
11-2 Study Guide and Intervention · 2015-06-26 · Areas of Triangles,Trapezoids, and Rhombi. ......
Transcript of 11-2 Study Guide and Intervention · 2015-06-26 · Areas of Triangles,Trapezoids, and Rhombi. ......
Exercises
Example
Chapter 11 15 Glencoe Geometry
Less
on
11-
2
11-2 Study Guide and InterventionAreas of Triangles, Trapezoids, and Rhombi
NAME ______________________________________________ DATE ____________ PERIOD _____
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Areas of Triangles The area of a triangle is half the area of a rectangle with the samebase and height as the triangle.
If a triangle has an area of A square units, a base of b units,
and a corresponding height of h units, then A � �12
�bh.
Find the area of the triangle.
A � �12�bh Area of a triangle
� �12�(24)(28) b � 24, h � 28
� 336 Multiply.
The area is 336 square meters.
Find the area of each figure.
1. 2.
3. 4.
5. 6.
7. The area of a triangle is 72 square inches. If the height is 8 inches, find the length of the base.
8. A right triangle has a perimeter of 36 meters, a hypotenuse of 15 meters, and a leg of 9 meters. Find the area of the triangle.
24 2418
10
21
1560
54
24
60�10
20
20
26
56
21
20 16
33
28 m
24 m
h
Z Y
X
b
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Example
Exercises
Chapter 11 16 Glencoe Geometry
11-2 Study Guide and Intervention (continued)
Areas of Triangles, Trapezoids, and Rhombi
NAME ______________________________________________ DATE ____________ PERIOD _____
Copyright ©
Glencoe/M
cGraw
-Hill, a division of T
he McG
raw-H
ill Com
panies, Inc.
Areas of Trapezoids and Rhombi The area of a trapezoid is the product of half theheight and the sum of the lengths of the bases. The area of a rhombus is half the product ofthe diagonals.
If a trapezoid has an area of A square units, bases of If a rhombus has an area of A square units andb1 and b2 units, and a height of h units, then diagonals of d1 and d2 units, then
A � �12
�h(b1 � b2). A � �12
�d1d2.
Find the area of the trapezoid.
A � �12�h(b1 � b2) Area of a trapezoid
� �12�(15)(18 � 40) h � 15, b1 � 18, b2 � 40
� 435 Simplify.
The area is 435 square meters.
Find the area of each quadrilateral.
1. 2.
3. 4.
5. 6.
7. The area of a trapezoid is 144 square inches. If the height is 12 inches, find the length ofthe median.
8. A rhombus has a perimeter of 80 meters and the length of one diagonal is 24 meters.Find the area of the rhombus.
28
12 24
13
1313
13
18
16
32
1632
12 60�
10
10
2020
40 m
18 m
15 m
d2 d1h
b2
b1
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Example 2Example 1
Exercises
Chapter 11 29 Glencoe Geometry
Less
on
11-
4
11-4 Study Guide and InterventionAreas of Composite Figures
NAME ______________________________________________ DATE ____________ PERIOD _____
Cop
yrig
ht ©
Gle
ncoe
/McG
raw
-Hill
, a
divi
sion
of T
he M
cGra
w-H
ill C
ompa
nies
, In
c.
Composite Figures A composite figure is a figure that can be seprated into regionsthat are basic figures. To find the area of a composite figure separate the figure into basicfigures of which we can find the area. The sum of the areas of the basic figures is the area ofthe figure.
Find the area of thecomposite figure.
The figure is a rectangle minus one half of a circle. The radius of the circle is one halfof 30 or 15.
A � lw � �12��r2
� 50(30) � 0.5�(15)2
� 1146.6 or about 1147 ft2
50 ft
30 ft
Find the area of theshaded region.
The dimensions of the rectangle are 10 centimeters and 30 centimeters. The areaof the shaded region is(10)(30) � 3�(52) � 300 � 75�
� 64.4 cm2
5 cm
Find the area of each figure. Round to the nearest tenth if necessary.
1. 2.
3. 4.
5. 6.
7. Refer to Example 2 above. Draw the largest possible square inside each of the threecircles. What is the total area of the three squares?
15 yd
35 yd64 m
20 m 20 m40 m
22 cm
42 cm
40 cm38 cm
14 cm 10 cm
40 in.
24 in.24 in.15 ft
34 ft
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