1. Class Greeting

2. Perimeters and Areas of figures in a Coordinate Plane
Chapter 9 – Lesson 4
Perimeters and Areas of figures in a Coordinate Plane

3. Objective
Find the perimeters and areas of figures in a coordinate plane.

4. 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.

5. Example 1A: Estimating Areas of Irregular Shapes in the Coordinate Plane
Estimate the area of the irregular shape.
The area is approximately
= 30 units2.
Count the number of squares inside the figure.
Use a  for a whole square and for a half square.
There are 23 whole squares and 15 half squares, so the area is about…

6. 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.

7. Example 2a: 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).
Step 1 Draw the polygon.
Step 2 Prove that EFGH is a parallelogram.
Use slopes to show that opposite sides are parallel.
slope of EF and GH = -1/3
slope of FG and HE = 2/3
EFGH is a by definition of parallelogram.

8. Example 2: Finding Perimeter and Area in the Coordinate Plane
Find the perimeter of the polygon with vertices E(–1, –1), F(2, –2), G(–1, –4), and H(–4, –3).
Step 1 Use the Distance Formula to find each side length.
Since EFGH is a , EF = GH, and FG = HE.
Perimeter of EFGH:

9. Example 2: Finding Perimeter and Area in the Coordinate Plane
Find the area of the polygon with vertices E(–1, –1), F(2, –2), G(–1, –4), and H(–4, –3).
Step 1 Cut EFGH into 2 triangles.
The base and height of each triangle is 3 units.
Step 2 Find the area of each .
Step 2 Find the area of EFGH.
Area of EFGH: 9

10. 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.

11. 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.

12. Check It Out! Example 2 Continued
are vertical lines.
The opposite sides are parallel, so HJKL is a parallelogram.

13. 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:

14. 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.

15. 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).
Step 1 Draw the polygon and close it in a rectangle.
Step 2 Area of rectangle:
A = bh = 8(6)= 48 units2.
Step 3 Area of triangles:
Step 4 Find the area of the polygon.
48 – 9 – 3 – 9 – 3 = 24 units2.

16. 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).
Area of triangles: a b d c
The area of the polygon is 96 – 12 – 24 – 2 – 10 = 48 units2.

17. Lesson Summary: Objectives
Find the perimeters and areas of figures in a coordinate plane.

18. Preview of the Next Lesson:
Objectives
Describe the effect on perimeter and area when one or more dimensions of a figure are changed.
Apply the relationship between perimeter and area in problem solving.

19. Kahoot!

20. Stand Up Please