Perimeter of Polygons & Circumference of Circles

Perimeter of Polygons & Circumference of Circles

What is Perimeter?

Peri means around or about

Meter is to measure

Perimeter is both the path around a shape and also a measure of the distance around it.

Multiple Choice

The distance around an object is called the

• area

• perimeter

• volume

• formula

Finding Perimeter

for polygons, just add up all the sides...

P = 3+6+6 = 15 miles

Multiple Select

Perimeter is....

• the distance around a polygon

• the sum of all sides of a polygon

• either a path that encompasses/surrounds/outlines a shape or its length.

• all the 2 dimensional space inside a polygon

Perimeter Formulas

Polygon Perimeter formulas show the addition or sum of all sides.

Because squares and rectangles have two or more congruent sides, the formulas reflect repeated addition as multiplication.

Rectangle Perimeter

If we add up all the sides, there are 2 W's and 2 L's

 $P=L+L+W+W$  

or

 $P=2L+2W$  

Multiple Choice

Find the PERIMETER of this figure.

• 25 cm

• 20 cm

• 10 cm

• 20 sq. cm

Multiple Choice

What is the perimeter?

• 9 units

• 12 sq units

• 12 units

• None of the above

Multiple Choice

What is the perimeter of the shaded figure?

• 28

• 24

• 22

• 26

Multiple Choice

Makena needs to build a rectangular fence for his bipi kāne. He wants to build a fence around a pen that is 40 feet long and 20 feet wide. How many feet of fence does he need?

• 800 feet

• 120 feet

• 60 feet

Square Perimeter

Since all sides are congruent in a square, the perimeter of a square is

 $P=s+s+s+s$  

or

 $P=4s$  

Multiple Choice

What is the perimeter of the square?

• 2

• 8

• 10

• 4

Multiple Choice

What is the perimeter if all sides are 4 inches?

• 4 in.
• 16 in. 
• 8 in. 

Perimeter of Regular Polygons

Since all sides are congruent in a regular polygon and since there are "n" sides, the perimeter for any Regular polygon is

 $P=n\times\left(s\right)$  

Multiple Choice

REGULAR in Maths means...

• Normal
• Two sides have the same length
• All sides are equal and all angles are equal
• It has right angles

Multiple Choice

What is the perimeter of this figure

• 22
• 21
• 18
• 20

Multiple Choice

What is the perimeter?

• 15
• 10
• 3

Perimeter of Polygons

see that for trapezoids, triangles and other simple polygons, the perimeter is just the sum of all sides

Multiple Choice

What is the perimeter of the shape?

• 4 in.
• 10 in. 
• 12 in. 

Multiple Choice

_{What is the perimeter?}

• 55 in

• 55 cm

• 55ft

• $55

Multiple Choice

_{What is the perimeter?}

• 13 cm

• 22 cm

• 26 cm

• 36 cm

Using Algebra with Perimeter Formulas

Given this Perimeter,

What is the value of side x?

Substitute

 we know P=20cm
and since (for this shape) 

       P= 4(x)

if we substitute 20 in for P
    20 = 4(x) 

 $\frac{20}{4}=\frac{4x}{4}$  

      $5=x$  

If the Perimeter of this Triangle is 38cm, What is x?

..start with what you know

P=38      also

P= x +(x+3) + (2x-5)

substitute
38 = x +(x+3) + (2x-5)

simplify
       38 = 4x-2
solve
   38+2 = 4x
      40 = 4x
       10 = x

check
       38=10+10+3+2(10)-5

Follow my steps....

If the Perimeter is 32 inches, what is w?

• P= (w-2)+(w-2)+(w-2)+(w-2)+(w-2)+(w+5)=(w+5)

• P = 4(w-2)+2(w+5)

• P = 4x-8 + 2w+10

• P = 6x +2

• 32 = 6x +2

• 30 = 6x

• 5 = w

Multiple Select

If the Perimeter is 46, Which of the following are true?

• P = x+(x+4)+(x+6)

• P = 3x+10

• 46 = 3x+10

• 36 = 3x

• 12 = x

Multiple Choice

What is the Perimeter if x is 4?

• 16

• 20

• 36

• 72

Multiple Choice

If the Perimeter is 20ft, what is n?

• 6ft

• 4ft

• 22ft

• 42ft

Multiple Choice

What is b if the Perimeter is 58 mm?

• 1

• 2

• 3

• 4

What is Circumference?

circum-- circle, around

ference-- to carry

..its the perimeter of a circle or ellipse

What is Pi again?

We have previously measured and defined pi as the ration of C:D

-so for any circle, the circumference is more than 3 times the diameter

Circumference Formulas

Circumference relates to Diameter

 $C=\pi\left(D\right)$   ...and since D= 2r

 $C=\pi\left(2r\right)$  ...or more commonly
 $C=2\pi r$  ... as it relates ro radius

Multiple Choice

What does "circumference" mean?

• Space a circle takes up
• Distance around a circle
• Line from one side of a circle to another
• Line from center of circle to side

Multiple Choice

Does this picture show the diameter or radius of a circle?

• Diameter

• Radius

Multiple Choice

What is the formula for circumference of a circle given the radius?

• $C=\pi r$
  

• $C=2\pi r$
  

• $C=2\pi D$
  

• $C=\pi r^2$
  

Multiple Choice

What is the formula for circumference of a circle given the diameter?

•  $C=\pi D$ 
  

•  $C=2\pi D$ 
  

•  $C=2\pi$ 
  

•  $C=\pi D^2$ 
  

Multiple Choice

Find the circumference of the circle

• 18.84 cm

• 75.36 cm

• 37.68 cm

• 3.14 cm

Multiple Choice

Find the circumference (to the nearest whole number)

• 88 in
• 44 in
• 116 square in
• None of the above

Multiple Choice

Daniel wants to buy cookies for her friend. The radius of a cookie is 5 inches. What is the cookie’s circumference?

• 10 in

• 2.5 in

• 15.7 in

• 31.4 in

Multiple Choice

Steven purchases a bowl. The diameter of the bowl is 14 cm. What is the circumference of the bowl?

• 28 cm

• 43.98 cm

• 87.96 cm

• 7 cm

Solving for r, D

• Pi has a value of approximately 3.14 which is needed to find Circumference

• if  $C=\pi D$       then       $D=\frac{C}{\pi}$  

• if   $C=2\pi r$         then          $r=\frac{C}{\left(2\pi\right)}$  

• be careful!   notice the parenthesis above?  when you have a product in a denominator, use parenthesis to avoid Order of Operations error in calculator

Multiple Choice

This Circular Infinity pool has a Circumference of 31.42ft. What is the radius of the pool?

• about 10 ft

• about 5 feet

• 3.142 ft

• looks to be about 6ft

Multiple Select

How wide is a size 7 basketball ?

• 9.4 inches

• 4.7 inches

• 23.9 cm

• 11.9 cm

Multiple Choice

The equatorial circumference of Earth is about 24,901 miles. What is the approximate diameter of the Earth at the equator?

• 7926 mi

• 3963 mi

• 78, 228 mi

• who can know this stuf?

Compound Perimeter

Shapes made from a combination of polygons are called Compound. We can fins the Perimeter by adding up the pieces along the outside...

What is the Perimeter of this compound shape?

Add up the sides

Start at a point and add up sides along the way, there are two sections that we arent given...? and to its right, call it top

9+4+?+6+(top)+12

? has to be 3 because 9-6= 3

top is (12-4) = 8

so P = 9+4+3+8+6+12

P= 34 cm

Multiple Choice

What is the missing side needed to find the Perimeter?

• 12m

• 9m

• 6m

• 3m

Multiple Choice

Find the Perimeter

• 144m

• 68m

• 62m

• 6m

What is the Perimter?

1 + 1 + semicircle

circle radius is 1 so its circumference would be C=3.14(D) = 3.14 in

The semicricle is half the Circumference so

1+ 1+ 1.57 = 3.57 inches

Multiple Choice

A half circle sits on a square. Which formula correctly solves for the Perimeter?

• $P=12+12+12+6\pi$
  

• $P=12+12+12+12+6\pi$

• $P=12+12+12+12\pi$

Multiple Select

Which formula Solves for the Perimeter of this shape?

• $P=2+2+\frac{3}{4}\left(2\pi\left(2ft\right)\right)$

• $P=2+2+\frac{3}{4}\left(4\pi ft\right)$

• $P=4+3\pi ft$

• $P=4+9.42ft$

Multiple Choice

What is the Perimeter of this shape?

• 9.42 ft

• 12.6 ft

• 16.6 ft

• 13.42 ft

Multiple Select

Which of these correctly solves for the Perimeter?

• $P=7+8+7+\frac{1}{2}\left(12\pi\right)$

• $P=22+6\pi$

• $P=28\pi$

Multiple Choice

What is the Perimeter?

• 88m

• 22 m

• 18.8 m

• 40.8 m

Over it

Kick your Fins up, all Pau!