Name ________________________________________ Date __________________ Class__________________
LESSON
10-4
Reteach
Perimeter and Area in the Coordinate Plane
One way to estimate the area of irregular shapes in the coordinate plane is to count the
squares on the grid. You can estimate the number of whole squares and the number of half
squares and then add.
The polygon with vertices A(−3, −1), B(−3, 3), C(2, 3), and
D(4, −1) is drawn in the coordinate plane. The figure is a
trapezoid. Use the Distance Formula to find the length of CD .
CD =
( 4 − 2)
2
+ ( −1 − 3 ) = 20 = 2 5
2
perimeter of ABCD: P = AB + BC + CD + DA
=4+5+2 5 +7
≈ 20.5 units
area of ABCD: A =
=
1
( b1 + b2 )( h )
2
1
( 5 + 7 )( 4 ) = 24 units2
2
Estimate the area of each irregular shape.
1.
2.
_________________________________________
________________________________________
Draw and classify each polygon with the given vertices. Find the perimeter
and area of each polygon.
3. F(−2, −3), G(−2, 3), H(2, 0)
4. Q(−4, 0), R(−2, 4), S(2, 2), T(0, −2)
_________________________________________
________________________________________
_________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
10-30
Holt McDougal Geometry
Name ________________________________________ Date __________________ Class__________________
LESSON
10-4
Reteach
Perimeter and Area in the Coordinate Plane continued
When a figure in a coordinate plane does not have an area formula, another
method can be used to find its area.
Find the area of the polygon with vertices N(−4, −1), P(−1, 3), Q(4, 3),
and R(2, −2).
Step 1
Draw the polygon and enclose it in a rectangle.
Step 2
Find the area of the rectangle and the areas of
the parts of the rectangle that are not included
in the figure.
rectangle: A = bh = 8 • 5 = 40 units2
Step 3
a: A =
1
1
bh = ( 3 )( 4 ) = 6 units2
2
2
b: A =
1
1
bh = ( 2 )( 5 ) = 5 units2
2
2
c: A =
1
1
bh = ( 6 )(1) = 3 units2
2
2
Subtract to find the area of polygon NPQR.
A = area of rectangle − area of parts not included in figure
= 40 − 6 − 5 − 3
= 26 units2
Find the area of each polygon with the given vertices.
5.
6.
_________________________________________
7. A(−1, −1), B(−2, 3), C(2, 4), D(4, −1)
________________________________________
8. H(3, 7), J(7, 2), K(4, 0), L(1, 1)
_________________________________________
________________________________________
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
10-31
Holt McDougal Geometry
3. P ≈ 19.8 units; A = 22 units2
Reteach
1. A ≈ 30 units2
2. A ≈ 35.5 units2
3.
4. P ≈ 18.3 units; A = 8 units2
triangle; P = 16 units; A = 12 units2
4.
square; P ≈ 17.9 units; A = 20 units2
5. m∠W = 117°; m∠X = 45°; m∠Y = 153°;
m∠Z = 45°
5. A = 29 units2
6. A = 20.5 units2
7. A = 18 units2
8. A = 21.5 units2
Challenge
1. A ≈ 0.063 units2
2. about 32
3. Answers will vary: ≈ 2
4. about 16
5. Answers will vary: ≈ 1
6. Answers will vary: ≈ 0
6. m∠F = 47°; m∠G = 105°; m∠H = 153°;
m∠I = 55°
Problem Solving
1. P ≈ 22.8 units; A = 28 units2
2. P ≈ 12.1 units; A = 4 units2
3. A = 31.5 units2
4. Possible answer: A ≈ 36 m2
5. C
6. F
7. D
Original content Copyright © by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.
A39
Holt McDougal Geometry