Transcript Slide 1

9-4
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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
Objective
Find the perimeters and areas of
figures in a coordinate plane.
In Lesson 9-3, 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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
Remember!
Holt Geometry
9-4
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 Geometry
9-4
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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
Example 2 Continued
slope of EF =
slope of GH =
slope of FG =
slope of HE =
Holt Geometry
The opposite sides
are parallel, so EFGH
is a parallelogram.
9-4
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 Geometry
9-4
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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
Example 3 Continued
Area of triangles:
a
d
b
c
The area of the polygon is 96 – 12 – 24 – 2 – 10 =
48 units2.
Holt Geometry
9-4
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 Geometry
9-4
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
4. Show that the two composite figures cover the
same area.
For both figures,
A = 3 + 1 + 2 = 6 units2.
Holt Geometry
9-4
Perimeter and Area in
the Coordinate Plane
IN-Class
Assignment
Worksheet
Reteach 9-4
Holt Geometry