Transcript Slide 1

9-4
Perimeter and Area in
the Coordinate Plane
Objective
Find the perimeters and areas of
figures in a coordinate plane.
Holt Geometry
9-4
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 Geometry
9-4
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 Geometry
9-4
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 Geometry
9-4
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 Geometry
9-4
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 Geometry
9-4
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, 1), B(2, 4), C(4, 1), and D(–2, –2).
Draw the polygon and
close it in a rectangle.
Area of rectangle:
A = bh = 8(6)= 48 units2.
Holt Geometry
9-4
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 Geometry
9-4
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 Geometry
9-4
Perimeter and Area in
the Coordinate Plane
Check It Out! 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