Name _______________________________________ Date __________________ Class __________________
10.1 Reading Strategies
Use a Table
Use the table below to help you find areas of triangles and quadrilaterals.
Find each measurement.
Figure
Diagram
Formula
A
triangle
Example
Find the area of a triangle with
b  12 cm and h  4 cm.
1
A  (12)(4) cm2
2
A  24 cm2
1
bh
2
Find the height of a parallelogram
with A  18 in2 and b  9 in.
A  bh
parallelogram
18  (9)h in.
h  2 in.
Find the area of a trapezoid with
b1  6 ft, b2  8 ft, and h  3 ft.
A
trapezoid
1
(6  8)(3) ft2
2
A  (7)(3) ft2
A  21 ft2
1
 b1  b2  h
2
A
Find the diagonal d2 of a kite with
A  36 cm2 and d1  8 cm.
rhombus
or kite
A
1
(8)d2 cm
2
36  4d2 cm
d2  9 cm
36 
1
d1d2
2
1.area of the parallelogram
2. area of the triangle
________________________________________
________________________________________
3. base of a triangle with A  150 ft and h  30 ft
__________________
4. area of a rhombus with d1  10 mm and d2  30 mm
__________________
5. height of a trapezoid with A  60 in , b1  3 in., and b2  7 in.
__________________
6. base of a parallelogram with A  28 cm and h  7 cm
__________________
2
2
2
Name _______________________________________ Date __________________ Class __________________
10.2 Reading Strategies
Vocabulary Development
The diagram below describes the parts of a regular polygon and how to use
those parts to find the area of the polygon.
A regular polygon has
all sides of equal length
and all interior angles of
equal measure.
The center of a regular
polygon is equidistant
from the vertices.
The apothem is the
distance from the center to
the side.
A central angle of a
regular polygon has its
vertex at the center, and
its sides pass through
consecutive vertices. The
sum of the measures of
all the central angles
equals 360°.
The area of a regular
polygon with apothem a and
perimeter P is:
1
A  aP
2
Example:
Each side of a regular
hexagon is 10 m. The apothem
is 5 3 m. Find the area.
• First find the perimeter.
P  6(10)  60 m
• Then substitute into the
formula.
1
A  5 3  60   259.8 m2
2


Answer the following.
1. What is true about the sides of a regular polygon?
________________________________________________________________________________________
2. How many central angles are in a regular octagon?
_________________
3. What is the perimeter of a regular nonagon with side length 8 feet?
_________________
Use the formula for the area of a regular polygon to find the area of each figure.
Round to the nearest tenth if necessary.
4.
5.
________________________________________
________________________________________
Name ________________________________________ Date __________________ Class __________________
10.3 Reading Strategies
Compare and Contrast
Finding areas of composite
figures by adding
Finding areas of composite
figures by subtracting
Compare
Both methods divide a figure into simple shapes.
Both methods involve multiple steps.
Contrast
How shape
is divided
The shaded area you are
asked to find is completely
made up of simple shapes
whose areas can be found
with a formula.
Description
The shaded area you
are asked to find is part
of another, larger figure
whose area can be found
with a formula.
How to
solve
Subtract the unshaded
area from the total area.
Add the areas of each
simple shape to find the
total area.
Answer the following.
1. The area of the white rectangle is 7 cm2.
What is the area of the shaded region?
________________________________________
Find the shaded area of each composite figure. Round to the nearest tenth if necessary.
2.
3.
Name ________________________________________ Date __________________ Class __________________
10.4 Reading Strategies
Follow a Procedure
Use the steps below to find the area of a polygon in the coordinate plane.
Find the area of a polygon with vertices A(1, 4), B(5, 2), C(1, 2), D(4, 0).
Step 1: Draw the polygon.
Step 2: Draw a rectangle around it. Make every side
touch a vertex.
Step 3: Find the area of the
rectangle.
A  9(6)  54 units2
Step 4: Find the area of each
triangle.
AXB: A 
1
(6)(2)  6 units2
2
DZC: A 
1
1
(3)(2)  3 units2 BYC: A  (6)(4)  12 units2
2
2
Step 5: Subtract the areas of
the triangles from the
area of the rectangle.
AWD: A 
1
(3)(4)  6 units2
2
54  6  6  3  12  27 units2
Complete the following.
1. Draw a polygon with vertices
A(3, 6), B(5, 2), C(2, 2), D(3, 2).
2. To find the area of the polygon, what would
you do next?
________________________________________
________________________________________
3. How do you know how large to make the
rectangle that encloses the polygon?
________________________________________________________________________________________
4. Find the area of the polygon.
________________________________________________________________________________________
Name ________________________________________ Date __________________ Class __________________
10.5 Reading Strategies
Use a Graphic Aid
The graphic aid below summarizes the effects of changing the dimensions of a figure
proportionally.
All dimensions of a
figure are multiplied
by a factor of a.
Perimeter or
Circumference
Area
Changes by a
factor of a2.
Changes by a
factor of a.
The perimeter of a
square with side length
5 ft is 20 ft.
Examples
The area of a square
with side length
5 ft is 25 ft2.
Each side of the square
is multiplied by 3.
Each side of the square
is multiplied by 3.
Now the perimeter is
4(5 • 3)  4(15)  60 ft.
The original perimeter
has tripled, or changed
by a factor of 3.
Now the perimeter is
(5 • 3)2  (15)2  225 ft2.
The original area has
been multiplied by
32, or 9.
Answer the following.
1. If the length and width of a rectangle are doubled, the perimeter changes
by a factor of _____________________.
2. The sides of an equilateral triangle are multiplied by 4.
The perimeter of the resulting triangle is 60 feet. What
is the perimeter of the original triangle?
_____________________
3. Each side of a square is doubled. What is the effect on the area of the square?
________________________________________________________________________________________
4. A new square with an area of 900 cm2 was created by multiplying each side of an old square with an
area of 36 cm2 by a certain number. What was the number?
_____________________
Name ________________________________________ Date __________________ Class __________________
10.6 Reading Strategies
Use a Table
Use the table to help you find different kinds of geometric probabilities.
Model
Diagram
Example
A point is chosen at random on XZ . Find the
probability that the point is on XY .
length
P
XY
5

XZ 14
Find the probability that the pointer does not
land on white.
angle
measure
P
360  60 300 5


360
360 6
Find the probability that a point chosen
randomly inside the rectangle is in the square.
Area of the rectangle:
A  bh  25(10) cm2  250 cm2
area
Area of the square:
A  s 2  (5)2 cm2  25 cm2
P
25
1

250 10
Use the information in the table to answer the following.
1. Look at the example for length. The probability that a point chosen
at random on XZ is on YZ can be written as P 
YZ
.
2. Write the probability described in Exercise 1 as a
percent to the nearest whole percent.
______________________
3. Look at the example for angle measure. What is the
probability that the pointer DOES land on white?
______________________
4. How is your answer to Exercise 3 related to the answer in the example? Why?
________________________________________________________________________________________
5. Look at the example for area. Find the probability that a point
chosen randomly inside the rectangle is in the parallelogram.
______________________