LESSON 6.3 – FINDING PERIMETER AND AREA IN THE COORDINATE

PLANE

CONCEPT: DISTANCE IN THE COORDINATE PLANE

EQ: HOW DO WE FIND AREA & PERIMETER IN THE COORDINATE

PLANE? (G.GPE.7)

VOCABULARY: DISTANCE FORMULA, POLYGON, AREA, PERIMETER

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 1

THINK-PAIR-SHARE• Think back to the distance

formula and when you used it. Take a minute and write down everything you remember about using the distance formula.

• With your partner, compare your notes to see if you missed anything.

• Wait to be called on and then share your answers with the class.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 2

INTRODUCTIONIn the previous lesson, the distance formula was used to find the distance between two given points. In this lesson, the distance formula will be applied to perimeter and area problems.

A polygon is a two-dimensional figure formed by three or more segments. We will use the distance formula to find the perimeter, or the sum of the lengths of all the sides of a polygon, and the area, the number of square units inside of a polygon, such as finding the amount of carpeting needed for a room.

Be sure to use the appropriate units (inches, feet, yards, etc.) with your answers.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 3

AREA OF A PARALLELOGRAM• A parallelogram includes shapes such as

squares, rectangles, rhombuses. • The area of a parallelogram is found using

the formula: Area = ) • The length of the base and height are found

using the distance formula. • The final answer must include the

appropriate label (units², feet², inches², meters², centimeters², etc.)

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 4

GUIDED PRACTICE, EXAMPLE 1Parallelogram ABCD has vertices A (-5, 4), B (3, 4), C (5, -1), and D (-3, -1). Calculate theperimeter and area of parallelogram ABCD.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 5

EXAMPLE 1, CONTINUEDWe need to find the length of all four sides before we can find the area and the perimeter. So we will use the distance formula:

• The length of is 8 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 6

EXAMPLE 1, CONTINUEDDistance formula:

• The length of is 5.39 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 7

EXAMPLE 1, CONTINUEDDistance formula:

• The length of is 8 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 8

EXAMPLE 1, CONTINUEDDistance formula:

• The length of is 5.39 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 9

EXAMPLE 1, CONTINUED • Find the perimeter by adding up all the sides:

Find the area by using the formula • or is the base and they are the same length

so • The height can be found by drawing a perpendicular

line straight up from D to side and down from B to side . • You can do this by counting the units or using the

distance formula • Finding the distance from D to the point and the

distance from B to the point where the perpendicular line touches at

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 10

EXAMPLE 1, CONTINUEDArea of a Parallelogram = • Base = 8 units• Height = 5 units• Area of a parallelogram =

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 11

AREA OF A TRIANGLE • The area of a triangle is found by using the

formula: Area =

• The height of a triangle is the perpendicular distance from a vertex to the base of the triangle.

• Determining the lengths of the base and the height is necessary if these lengths are not stated in the problem.

• The final answer must include the appropriate label (units², feet², inches², meters², centimeters², etc.)

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 12

GUIDED PRACTICE, EXAMPLE 2Triangle ABC has vertices A (2, 1), B (4, 5), and C (7, 1). Calculate the perimeterand area of triangle ABC.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 13

EXAMPLE 2We need to find the length of all three sides before we can find the area and the perimeter. So we will use the distance formula:

• The length of is 4.47 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 14

EXAMPLE 2, CONTINUEDDistance Formula:

• The length of is 5 units.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 15

EXAMPLE 2, CONTINUEDDistance Formula:

5

• The length of is 5 units.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 16

EXAMPLE 2, CONTINUED

• Find the perimeter by adding up all the sides:

Find the area by using the formula • is the base so • The height can be found by drawing a perpendicular

line straight down from B to side . • Then find the distance from B to the point where the

perpendicular line touches at • You can do this by counting the units or using the

distance formula

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 17

EXAMPLE 2, CONTINUEDArea of a Triangle = • Base = 5 units• Height = the distance from to = 4

• Area of a triangle =

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 18

AREA OF A TRAPEZOID • The area of a trapezoid is found by using the

formula: Area =

• A trapezoid has a smaller base () and a larger base () . You will need to add both bases together in the area formula.

• The height of a trapezoid is the perpendicular distance from a vertex to the base of the trapezoid.

• The final answer must include the appropriate label (units², feet², inches², meters², centimeters², etc.)

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 19

GUIDED PRACTICE, EXAMPLE 3Trapezoid EFGH has vertices E (-8, 2), F (-4, 2), G (-2, -2), and H (-10, -2). Calculate theperimeter and area of trapezoid EFGH.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 20

EXAMPLE 3, CONTINUEDWe need to find the length of all four sides before we can find the area and the perimeter. So we will use the distance formula:

• The length of is 4 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 21

EXAMPLE 3, CONTINUEDDistance formula:

• The length of is 4.47 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 22

EXAMPLE 3, CONTINUEDDistance formula:

• The length of is 8 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 23

EXAMPLE 3, CONTINUEDDistance formula:

• The length of is 4.47 units

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 24

EXAMPLE 3, CONTINUED • Find the perimeter by adding up all the sides:

• Find the area by using the formula • So .• The height can be found by drawing a perpendicular

line straight down from E to side or from F to side . • You can do this by counting the units or using the

distance formula

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 25

EXAMPLE 3, CONTINUEDArea of a Trapezoid =• units• units• Height = 4 units• Area of a trapezoid =

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 26

YOU TRY! Find the perimeter and area of rectangle JKLM. • Reminder: Perimeter = sum of all the sides

Area =

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 27

3-2-13 – List three things you learned from this lesson.

2 – List two things you used in this lesson that you learned in previous lessons.

1 – Write one question you still have about area and perimeter of polygons.

6 . 2 . 2 : C A L C U L A T I N G P E R I M E T E R A N D A R E A 28