1. 10-4 Perimeter and Area in the Coordinate Plane Warm Up
Lesson Presentation
Lesson Quiz
Holt McDougal Geometry
Holt Geometry

2. Warm Up
Use the slope formula to determine the slope of each line. 1. 2.
3. Simplify

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

4. Check It Out! Example 1
Use a composite figure to estimate the shaded area. The grid has squares with side lengths of 1 ft.
Draw a composite figure that approximates the irregular shape. Find the area of each part of the composite figure.

5. Check It Out! Example 1 Continued
area of triangle:
area of half circle:
area of rectangle:
A = lw = (3)(2) = 6 ft2
The shaded area is about 12 ft2.

6. 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.

7. Example 1A: Estimating Areas of Irregular Shapes in the Coordinate Plane
Estimate the area of the irregular shape.

8. 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
= 30 units2.

9. 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

10. Check It Out! Example 1B
Estimate the area of the irregular shape.
There are approximately 33 whole squares and 9 half squares, so the area is about 38 units2.

11. Remember!

12. 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.

13. Example 2 Continued
Step 2 EFGH appears to be a parallelogram. To verify this, use slopes to show that opposite sides are parallel.

14. Example 2 Continued
slope of EF =
slope of GH =
slope of FG =
The opposite sides are parallel, so EFGH is a parallelogram.
slope of HE =

15. 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:

16. 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.

17. Check It Out! Example 3
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.

18. Check It Out! Example 3 Continued
Step 2 HJKL appears to be a parallelogram. To verify this, use slopes to show that opposite sides are parallel.

19. Check It Out! Example 3 Continued
are vertical lines.
The opposite sides are parallel, so HJKL is a parallelogram.

20. Check It Out! Example 3 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:

21. Check It Out! Example 3 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.

22. Example 4: 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.

23. Example 4 Continued
Area of triangles:
The area of the polygon is 48 – 9 – 3 – 9 – 3 = 24 units2.

24. Check It Out! Example 5
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.

25. Check It Out! Example 5 Continued
Area of triangles: a b d c
The area of the polygon is 96 – 12 – 24 – 2 – 10 = 48 units2.