Geometry:

Perimeter

and Area Melissa Kramer

Laingsburg High School

Laingsburg, Michigan

A polygon is a

closed plane

figure formed by

three or more

segments

Each segment intersects

exactly two others at their

endpoints.

Names of Polygons

# of Sides Name

3 Triangle

4 Quadrilateral

5

6

7 Heptagon

8

9 Nonagon

10

Names of Polygons

# of Sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6

7 Heptagon

8

9 Nonagon

10

Names of Polygons

# of Sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8

9 Nonagon

10

Names of Polygons

# of Sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10

Names of Polygons

# of Sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10 Decagon

Two Types of Polygons

Concave: Has at least one corner

“pushed in” toward the center

Convex: All corners point away from the

center

Essential Understanding: Perimeter and area are two DIFFERENT

ways of measuring geometric figures

The perimeter (notated “P”) of a

polygon is the sum of the lengths of its

sides

The area (notated “A”) of a polygon is

the number of square units it encloses

Many figures have formulas to calculate

their perimeter and area.

Which do you need to know: area

or perimeter?

The amount of carpet for the basement floor

Area

The amount of fence for a dog run

Perimeter

The amount of paint for the bedroom

Area

The amount of Halloween lights to hang around the window

Perimeter

General Formulas

Problem 1

You want to frame a 5 in by 7 in picture with a 1-in-wide frame.

What is the perimeter of the picture?

What is the perimeter of the outside edge of the frame?

5 in

7 in

9 in

Problem 1

Perimeter of a

rectangle has a formula: P=2l + 2w

P=2(5 in) + 2(7 in)

P=10 in + 14 in

Perimeter of the

picture is 24 inches

5 in

7 in

9 in

Problem 1

Perimeter of a

rectangle has a formula: P=2l + 2w

P=2(7 in) + 2(9 in)

P=14 in + 18 in

Perimeter of the

picture is 32 inches

5 in

7 in

9 in

Circles have special notation

and formulas

is the notation for circle. The

point that represents the center of

the circle is listed to the right of

the notation

How is W read?

Circle with center W

Circles and Pi

The formulas for a circle involve the special number pi (). Pi is the ratio

of any circle’s circumference

(perimeter) to its diameter. Pi is an

irrational number.

= 3.1415926…

A close approximation is 22

7

Problem 2 What is the

circumference and

area of the circle

at the right?

Problem 2 15 inches is the

diameter, so we’ll need

to use the

circumference formula

with “d”

𝐶 = 𝜋(𝑑)

𝐶 = 𝜋 15 𝑖𝑛

𝐶 = 15𝜋 𝑖𝑛

This answer is exact

Problem 2 15 inches is the

diameter, so we’ll need

to use the

circumference formula

with “d”

𝐶 = 𝜋(𝑑)

𝐶 = 𝜋 15 𝑖𝑛

𝐶 = 15𝜋 𝑖𝑛 ≈ 47.1 𝑖𝑛𝑐ℎ𝑒𝑠

This answer is

approximate

Problem 2 What is the

circumference and

area of the circle

at the right?

The area formula

needs the radius,

which is one-half

the diameter

𝑟 = 7.5 𝑖𝑛

Problem 2 What is the

circumference and area

of the circle at the right?

𝐴 = 𝜋𝑟2

𝐴 = 𝜋7.52

𝐴 ≈ 176.7 𝑖𝑛2

This is the approximate

answer

Finding Area of a Rectangle

You are designing

a poster that will

be 3 yd wide and 8

ft high. How much

paper do you

need to make the

poster? Give your

answer to the

nearest square

foot.

Your units must be

the same.

1 𝑦𝑑 = 3 𝑓𝑡

3 𝑦𝑑 = 9 𝑓𝑡

Finding Area of a Rectangle

Use the area for a

rectangle formula

𝐴 = 𝑙 𝑤

𝐴 = 9 𝑓𝑡 8 𝑓𝑡

𝐴 = 72 𝑓𝑡2

You need 72 𝑓𝑡2 of

paper to make the

poster

Your units must be

the same.

1 𝑦𝑑 = 3 𝑓𝑡

3 𝑦𝑑 = 9 𝑓𝑡

The units of the

floor plan at the

right are in feet.

Find the perimeter

and area of each

room.

a. the kitchen

b. the bedroom

c. the bathroom

d. the closet