Holt Geometry

9-4 Perimeter and Area inthe Coordinate Plane

Warm UpUse the slope formula to determine the slope of each line.

1.

2.

3. Simplify

Holt Geometry

9-4 Perimeter and Area inthe Coordinate Plane

9-4 Perimeter and Area inthe Coordinate Plane

Holt Geometry

Holt Geometry

9-4 Perimeter and Area inthe Coordinate Plane

Estimate the area of the irregular shape.

Example 1A: Estimating Areas of Irregular Shapes in the Coordinate Plane

Holt Geometry

9-4 Perimeter and Area inthe 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 Geometry

9-4 Perimeter and Area inthe 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 Geometry

9-4 Perimeter and Area inthe 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 Geometry

9-4 Perimeter and Area inthe 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.

Example 2: Finding Perimeter and Area in the Coordinate Plane

Step 1 Draw the polygon.

Holt Geometry

9-4 Perimeter and Area inthe 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 inthe Coordinate Plane

Example 2 Continued

slope of EF =

slope of FG =

slope of GH =

slope of HE =The opposite sides are parallel, so EFGH is a parallelogram.

Holt Geometry

9-4 Perimeter and Area inthe 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 inthe 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 inthe 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 inthe 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 inthe 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 Geometry

9-4 Perimeter and Area inthe Coordinate Plane

P619 #2-8 evens

Holt Geometry

9-4 Perimeter and Area inthe 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 inthe 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.