Holt McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane10-4 Perimeter and Area in

the Coordinate Plane

Holt Geometry

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

Holt McDougal Geometry

Holt McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

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

1.

2.

3. Simplify

Holt McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

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

Objective

Holt McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

In Lesson 10-3, you estimated the area ofirregular 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 McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

Estimate the area of the irregular shape.

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

Holt McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

Remember!

Holt McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 Perimeter and Area inthe 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 McDougal Geometry

10-4 Perimeter and Area inthe 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 McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

Check It Out! Example 2 Continued

are vertical lines.

The opposite sides are parallel, so HJKL is a parallelogram.

Holt McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

Step 3 Since HJKL is a parallelogram, HJ = KL, and JK = LH.

Use the Distance Formula to find each side length.

perimeter of EFGH:

Check It Out! Example 2 Continued

Holt McDougal Geometry

10-4 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 McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

Find the area of the polygon with vertices A(–4, 0), B(2, 3), C(4, 0), and D(–2, –3).

Example 3: Finding Areas in the Coordinate Plane by Subtracting

Draw the polygon and close it in a rectangle.

Area of rectangle:

A = bh = 8(6)= 48 units2.

Holt McDougal Geometry

10-4 Perimeter and Area inthe Coordinate Plane

Example 3 Continued

Area of triangles:

The area of the polygon is 48 – 9 – 3 – 9 – 3 = 24 units2.

Holt McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 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 McDougal Geometry

10-4 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