Perimeter
andand
AreaArea
in
Perimeter
in
10-4
10-4the Coordinate Plane
the Coordinate Plane
Warm Up
Lesson Presentation
Lesson Quiz
HoltMcDougal
GeometryGeometry
Holt
10-4
Perimeter and Area in
the Coordinate Plane
Warm Up
Use the slope formula to determine the
slope of each line.
1.
2.
3. Simplify
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Objective
Find the perimeters and areas of
figures in a coordinate plane.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
In Lesson 10-3, you estimated the area of
irregular shapes by drawing composite figures that
approximated the irregular shapes and by using area
formulas.
Another method of estimating area is to use a grid
and count the squares on the grid.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 1: Estimating Areas of Irregular Shapes in
the Coordinate Plane
Estimate the area of the irregular shape.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 1A Continued
Method 1: Draw a composite
figure that approximates the
irregular shape and find the
area of the composite figure.
The area is approximately
4 + 5.5 + 2 + 3 + 3 + 4 +
1.5 + 1 + 6 = 30 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 1A Continued
Method 2: Count the number
of squares inside the figure,
estimating half squares. Use a
 for a whole square and a
for a half square.
There are approximately 24
whole squares and 14 half
squares, so the area is about
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 1
Estimate the area of the irregular shape.
There are approximately 33
whole squares and 9 half
squares, so the area is
about 38 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Remember!
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 2: Finding Perimeter and Area in the
Coordinate Plane
Draw and classify the polygon with vertices
E(–1, –1), F(2, –2), G(–1, –4), and H(–4, –3).
Find the perimeter and area of the polygon.
Step 1 Draw the polygon.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 2 Continued
Step 2 EFGH appears to be a
parallelogram. To verify this,
use slopes to show that
opposite sides are parallel.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 2 Continued
slope of EF =
slope of GH =
slope of FG =
slope of HE =
The opposite sides are parallel, so EFGH is
a parallelogram.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 2 Continued
Step 3 Since EFGH is a parallelogram, EF = GH,
and FG = HE.
Use the Distance Formula to find each side length.
perimeter of EFGH:
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 2 Continued
To find the area of EFGH, draw a line to divide EFGH
into two triangles. The base and height of each
triangle is 3. The area of each triangle is
The area of EFGH is 2(4.5) = 9 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 2
Draw and classify the polygon with vertices
H(–3, 4), J(2, 6), K(2, 1), and L(–3, –1). Find
the perimeter and area of the polygon.
Step 1 Draw the polygon.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 2 Continued
Step 2 HJKL appears to be a
parallelogram. To verify this,
use slopes to show that
opposite sides are parallel.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 2 Continued
are vertical lines.
The opposite sides
are parallel, so HJKL
is a parallelogram.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 2 Continued
Step 3 Since HJKL is a parallelogram, HJ = KL,
and JK = LH.
Use the Distance Formula to find each side length.
perimeter of EFGH:
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 2 Continued
To find the area of HJKL, draw a line to divide HJKL
into two triangles. The base and height of each
triangle is 3. The area of each triangle is
The area of HJKL is
2(12.5) = 25 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 3: Finding Areas in the Coordinate Plane by
Subtracting
Find the area of the polygon with vertices
A(–4, 0), B(2, 3), C(4, 0), and D(–2, –3).
Draw the polygon and
close it in a rectangle.
Area of rectangle:
A = bh = 8(6)= 48 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Example 3 Continued
Area of triangles:
The area of the polygon is 48 – 9 – 3 – 9 – 3 = 24 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 3
Find the area of the polygon with vertices
K(–2, 4), L(6, –2), M(4, –4), and N(–6, –2).
Draw the polygon and
close it in a rectangle.
Area of rectangle:
A = bh = 12(8)= 96 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Check It Out! Example 3 Continued
Area of triangles:
a
b
d
c
The area of the polygon is 96 – 12 – 24 – 2 – 10 =
48 units2.
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Lesson Quiz: Part I
1. Estimate the area of the irregular shape.
25.5 units2
2. Draw and classify the polygon
with vertices L(–2, 1), M(–2, 3),
N(0, 3), and P(1, 0). Find the
perimeter and area of the
polygon.
Kite; P = 4 + 2√10 units;
A = 6 units2
Holt McDougal Geometry
10-4
Perimeter and Area in
the Coordinate Plane
Lesson Quiz: Part II
3. Find the area of the polygon with vertices
S(–1, –1), T(–2, 1), V(3, 2), and W(2, –2).
A = 12 units2
Holt McDougal Geometry