Exercises

Example

Chapter 11 15 Glencoe Geometry

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on

11-

2

11-2 Study Guide and InterventionAreas of Triangles, Trapezoids, and Rhombi

NAME ______________________________________________ DATE ____________ PERIOD _____

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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

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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

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on

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11-4 Study Guide and InterventionAreas of Composite Figures

NAME ______________________________________________ DATE ____________ PERIOD _____

Cop

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ht ©

Gle

ncoe

/McG

raw

-Hill

, a

divi

sion

of T

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cGra

w-H

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, In

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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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