Length
GH
=
∣
8
−
2
∣
=
6
Ruler Postulate (Postulate 1.1)
Width
GK
=
∣
7
−
2
∣
=
5
Ruler Postulate (Postulate 1.1)
The shed has a length of 6 feet and a width of 5 feet.
Step 2
Substitute the values for the length and width into the formula for
the area of a rectangle.
A
=
Ὑ
w
Write the formula for area of a rectangle.
=
(
6
)(
5
)
Substitute.
=
30
Multiply.
So, the area of the floor of the shed is 30 square feet.
4.
Look Back
Make sure your answer makes sense in the context of the problem.
Because you are finding an area, your answer should be in square units. An
answer of 30 square feet makes sense in the context of the problem.
✓
Monitoring Progress
Help in English and Spanish at
BigIdeasMath.com
11.
You are building a patio in your school’s courtyard. In the diagram at the left, the
coordinates represent the four vertices of the patio. Each unit in the coordinate
plane represents 1 foot. Find the area of the patio.
1 ft
1 ft
x
y
2
M
(2,
2)
R
(2,
-3)
P
(6,
-3)
N
(6,
2)

34
Chapter 1
Basics of Geometry
Tutorial Help in English and Spanish at
BigIdeasMath.com
Exercises
1.4
1.
COMPLETE THE SENTENCE
The perimeter of a square with side length
s
is
P
=
____.
2. WRITING What formulas can you use to find the area of a triangle in a coordinate plane?
3.
4.
5.
6.
In Exercises 7–12, find the perimeter of the polygon
with the given vertices.
(See Example 2.)
7.
G
(2, 4),
H
(2,
−
3),
J
(
−
2,
−
3),
K
(
−
2, 4)
8.
Q
(
−
3, 2),
R
(1, 2),
S
(1,
−
2),
T
(
−
3,
−
2)
9.
U
(
−
2, 4),
V
(3, 4),
W
(3,
−
4)
10.
X
(
−
1, 3),
Y
(3, 0),
Z
(
−
1,
−
2)
11.
x
y
4
2
4
2
−
2
−
4
L
(1, 4)
M
(4, 0)
N
(2, 0)
P
(
−
1,
−
2)
12.
x
y
2
4
−
2
−
4
A
(0, 4)
D
(0,
−
2)
E
(
−
2, 2)
F
(
−
2, 4)
B
(2, 0)
C
(2,
−
2)
In Exercises 13–16, find the area of the polygon with the
given vertices.
(See Example 3.)
13.
E
(3, 1),
F
(3,
−
2),
G
(
−
2,
−
2)
14.
J
(
−
3, 4),
K
(4, 4),
L
(3,
−
3)
15.
W
(0, 0),
X
(0, 3),
Y
(
−
3, 3),
Z
(
−
3, 0)
16.
N
(
−
2, 1),
P
(3, 1),
Q
(3,
−
1),
R
(
−
2,
−
1)
In Exercises 17–24, use the diagram.
x
y
4
2
−
4
−
6
−
2
4
6
2
−
2
−
4
B
(0, 3)
A
(
−
5, 4)
F
(
−
2, 1)
E
(2,
−
3)
D
(4,
−
5)
C
(4,
−
1)
17.
Find the perimeter of
△
CDE.
18.
Find the perimeter of rectangle
BCEF.
19.
Find the perimeter of
△
ABF.
20.
Find the perimeter of quadrilateral
ABCD.
21.
Find the area of
△
CDE.
22.
Find the area of rectangle
BCEF.
23.
Find the area of
△
ABF.
24.
Find the area of quadrilateral
ABCD.
Monitoring Progress and Modeling with Mathematics

Section 1.4
Perimeter and Area in the Coordinate Plane
35
ERROR ANALYSIS
In Exercises 25 and 26, describe and
correct the error in finding the perimeter or area of
the polygon.
25.
26.
A
(4, 3)
B
(5, 1)
C
(1, 1)
x
y
2
4
−
2
2
6
4
b
=
∣
5
−
1
∣
=
4
h
=
√
——
(5
−
4)
2
+
(1
−
3)
2
=
√
—
5
≈
2.2
A
=
1
—
2
bh
≈
1
—
2
(4)(2.2)
=
4.4
The area is about 4.4 square units.
✗
In Exercises 27 and 28, use the diagram.
x
y
2
−
2
2
−
2
Q
(2, 1)
P
(
−
2, 1)
27.
Determine which point is the remaining vertex of a
triangle with an area of 4 square units.
A
R
(2, 0)
B
S
(
−
2,
−
1)
C
T
(
−
1, 0)
D
U
(2,
−
2)
28.
Determine which points are the remaining vertices of
a rectangle with a perimeter of 14 units.
A
A
(2,
−
2) and
B
(2,
−
1)
B
C
(
−
2,
−
2) and
D
(
−
2, 2)
C
E
(
−
2,
−
2) and
F
(2,
−
2)
D
G
(2, 0) and
H
(
−
2, 0)
29.
USING STRUCTURE
Use the diagram.
x
y
4
−
2
4
2
−
2
K
(4, 4)
L
(4, 0)
H
(2, 0)
G
(2, 2)
J
(0, 4)
E
(0, 0)
F
(0, 2)
a.
Find the areas of square
EFGH
and square
EJKL
.
What happens to the area when the perimeter of
square
EFGH
is doubled?
b.
Is this true for every square? Explain.
30.
MODELING WITH MATHEMATICS
You are
growing zucchini plants in your garden. In the
figure, the entire garden is rectangle
QRST
. Each
unit in the coordinate plane represents 1 foot.
(See Example 4.)
R
(7, 13)
Q
(1, 13)
U
(1, 4)
T
(1, 1)
S
(7, 1)
W
(4, 1)
V
(4, 4)
x
y
4
2
6
8
10
12
14
4
2
8
6
10
a.
Find the area of the garden.
b.
Zucchini plants require 9 square feet around each
plant. How many zucchini plants can you plant?
c.
You decide to use square
TUVW
to grow lettuce.
You can plant four heads of lettuce per square foot.
How many of each vegetable can you plant?
Explain.
x
y
4
2
2
4
−
2
P
=
2
Ὑ
+
2
w
=
2(4)
+
2(3)
=
14
The perimeter is 14 units.
✗