Geometry Part 1B
Download
1 / 30

Geometry Part 1B - PowerPoint PPT Presentation


  • 274 Views
  • Uploaded on

Geometry Part 1B Perimeter By Julia Arnold, Dick Gill and Marcia Tharp for Elementary Algebra Math 03 online. Perimeter is the distance around an object.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Geometry Part 1B' - Gideon


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Slide1 l.jpg
Geometry Part 1BPerimeterByJulia Arnold, Dick Gill and Marcia Tharpfor Elementary Algebra Math 03 online


Slide2 l.jpg

Perimeter is the distance around an object.

If the object is arectangle, then it has 4 sides and opposite sides are equal in length and parallel to each other.The formula for its perimeter is

P = 2L + 2W where L is length and W is width of the rectangle.

If the object is acircle, we call the perimeter the circumference and ancient mathematicians found its formula to be .


Slide3 l.jpg

In many perimeter problems involving rectangles, you may

be asked to find the dimensions. The dimensions of a rectangle

are the width by length. For example, picture frames are

categorized by their dimensions, such as 8 by 10, or 11 by 14.

The sum of the dimensions represents half of the perimeter.

The dimensions are only half the perimeter.

A picture frame that is an 8 by 10 would have a perimeter of

2(8 + 10) or 36 inches.What would be the perimeter of an

11 by 14 picture frame?


Slide4 l.jpg

Answer: An 11 by 14 inch picture frame would have a

perimeter of 2(11+14) = 50 inches.


Slide5 l.jpg

Example 1: Suppose we have a rectangle with a perimeter of 26 inches.We are told that the length is 10 more than twice the width.Can we find the dimensions of the rectangle?

Define the variables:

Let x = width, then 10 + 2x = length

The sum of width and length is half the perimeter, thus...

x + 10 + 2x = 26/2

3x + 10 = 13

3x = 3

x = 1 inch This is the width.

2x + 10 = 2(1) + 10 = 12 which is the length.

The dimensions are 1 by 12.


Slide6 l.jpg

Example 2. The perimeter of a rectangular lot is 440 meters. If the length is 150 m. find the width.

Let x = width

2L + 2W = P

2(150) + 2x = 440

300 + 2x = 440

300 + 2x - 300 = 440 - 300

2x = 140

x = 70 m, the width

or L + W = P/2

150 + x = 220

x = 220 - 150= 70 m, the width


Slide7 l.jpg

Example 3. The length of a rectangle is 10 more than twice the width. Find the length and the width if the perimeter is 56 inches.

Go ahead and guess now. Remember that 2L + 2W = P or

2(L+W) = P or L + W = P/2

Let x = the width

2x + 10 = the length

2L + 2W = P

2(2x + 10) + 2x = 56

4x + 20 + 2x = 56

6x + 20 - 20 = 56 - 20

6x = 36

x = 6 inches, the width

2x + 10 = 2(6) + 10 = 22 inches, the length

Or 2x + 10 + x = 56/2

3x + 10 = 28

3x = 18

x = 6 inches, the width

2(6)+10=22 inches, the length


Slide8 l.jpg

Example 4. The perimeter of a triangle is 85 cm. If the middle side is 5 cm. larger than the smallest side and the large side is twice the

smallest side, find each side.

2L + 2W = P only works for rectangles. Perimeter is the distance

around the outside of the figure. For a triangle then, the perimeter

is the sum of the three sides.

Let x = the smallest side

x + 5 = the middle side

2x = the largest side

x + (x + 5) + 2x = 85

4x + 5 - 5 = 85 - 5

4x = 80

x = 20 cm, the shortest side

x + 5 = 25 cm, the middle side and 2x = 40 cm


Slide9 l.jpg

How would you find the perimeter of this middle side is 5 cm. larger than the smallest side and the large side is twice the

architect’s home plan?


Slide11 l.jpg

Example 5: middle side is 5 cm. larger than the smallest side and the large side is twice the

20’

10’

This shape consists of a rectangle with two

Overlapping circles. Can we find the perimeter

If we know the dimensions of the rectangle?


Slide12 l.jpg

This shows the outside of the figure which middle side is 5 cm. larger than the smallest side and the large side is twice the

Is the perimeter that we must find. The perimeter

Is actually two lengths of the rectangle and two

Semi-circles.

20’

10’

We need the formula for the circumference of a circle which is C = 2 pi( r) Where r is the radius of the circle.

An alternate formula is C = pi d where d is the diameter of the circle. pi is the number which is approximated by 3.141592654


Slide13 l.jpg

Since the two semicircles are the same size the two parts make one complete circle. Thus the perimeter is

P = 20 + 20 + (10) = 40 + 10

Which is approximately 71.4’

20’

10’

Is the Greek symbol for Pi


Slide14 l.jpg

Other four sided figures which have opposite sides equal are:

parallelograms which have opposite sides parallel as well.

A rhombus which has four equal sides with opposite sides parallel


Slide15 l.jpg

What is the difference between rectangles, squares, parallelograms and rhombuses?

A square is a rectangle which has 4 equal sides and every angle is a right angle.

Rectangle

Square


Slide16 l.jpg

A parallelograms and rhombuses? rectangle is a parallelogram because opposite sides are equal in both and opposite sides are parallel in both.

The difference between the two is the rectangle has four right angles.

A parallelogram has no right angles.


Slide17 l.jpg

A parallelograms and rhombuses? square is a rhombus, because all four sides are equal and opposite sides are parallel

A rhombus is also a parallelogram because opposite sides are equal and parallel.

A square has

four right angles.

A rhombus has no right angles.


Slide18 l.jpg

If a figure is called a parallelograms and rhombuses? quadrilateral, then that means it

has four sides, but they could all be different measurements and they do not have to have opposite sides parallel.


Slide19 l.jpg

Your Turn parallelograms and rhombuses?

Work out the problems on the next

slides to see if you understand this

concept.


Slide20 l.jpg

3. A rectangular lot has a perimeter of 80 feet and length of 25 feet.

What is the width of the lot?

Complete Solution

4. Mr. Green wants to make a rectangular garden plot. He wants the length to be twice the width plus 3 feet. If the perimeter of the lot is 66 feet, what are the dimensions of the lot?

Complete Solution

5. Mr. Fixit wants to fence in a rectangular lot where one side will be the wall of his barn. He has 60 feet of fencing available. If the length is 4 feet less than twice the width. What are the dimensions of the lot?

Complete Solution


Slide21 l.jpg

6. A quadrilateral has sides measuring 16.5 in. , 17.3 in. , 21.8 in., 29.2 in.

What is its perimeter?

7. An Equilateral triangle has a side measuring 1.28 cm. What is its perimeter?

8. An Isosceles triangle has its equal side measuring 15.4 in. and its 3rd side measuring 23.9 in. What is its perimeter?

9. A square measures 1.63 m. What is its perimeter?

10. A rhombus measures 8.06 ft. on a side. What is its perimeter?

11. A parallelogram measures 47.2 on one side and 36.8 on another. What is its perimeter?

12. A rectangle has dimensions 57.9 by 39.8 in. What is its perimeter?

When complete go to next slide.

Complete Solutions


Slide22 l.jpg

13. Find the circumference of the circle whose radius is 14.3 cm.

Round to the nearest tenth.

14. Find the circumference of the circle whose diameter is 8.4 in.

Round to the nearest tenth.

Find the perimeters of the indicated figures:

15.

6 ft.

17.

7 ft.

12 ft.

28 cm.

11 ft.

12 cm.

18 ft.

60.8 ft.

14 cm.

16.

46.0 ft.

16 cm

Complete Solutions

12 cm


Slide23 l.jpg

Find the perimeter of this figure. 14.3 cm.

18.

15.3 cm.

19.6 cm

Complete Solutions


Slide24 l.jpg

Length + width = 1/2 perimeter

150 + x = 440/2

150 + x = 220

x = 70

The width is 70

Return to Problems

  • 2. The perimeter of a triangle is 85 cm. If the middle side is 5 cm. larger than the smallest side and the large side is twice the smallest side, find each side.

X = smallest side

x + 5 = middle side

2x = largest side

x + x + 5 + 2x = 85

4x + 5 = 85

4x = 80

x = 20

X = 20

x + 5 = 25

2x = 40

check

20 + 25 + 40 = 85


Slide25 l.jpg

Let x = width length is 150 m. find the width.

x + 25 = 80/2

x + 25 = 40

x = 15 The width of the lot is 15 feet.

4. Mr. Green wants to make a rectangular garden plot. He wants the length to be twice the width plus 3 feet. If the perimeter of the lot is 66 feet, what are the dimensions of the lot?

Return to Problems

Let x = width, length = 2x + 3

x + 2x + 3 = 66/2

3x + 3 = 33

3x = 30

x = 10 2x + 3 = 23 The dimensions are 10 x 23 feet.


Slide26 l.jpg

Barn Wall length is 150 m. find the width.

Three sides fencing

x

x

Let x = width

2x – 4 = length

2x-4

Add 3 sides: x + x + 2x – 4 = 60

4x – 4 = 60

4x = 64

x = 16

2x – 4 = 28

The dimensions are

16 by 28 feet.

Return to Problems


Slide27 l.jpg

. length is 150 m. find the width.

6. A quadrilateral has sides measuring 16.5 in. , 17.3 in. , 21.8 in., 29.2 in.

What is its perimeter? 84.8 inches

7. An Equilateral triangle has a side measuring 1.28 cm. What is its perimeter? 1.28*3= 3.84 cm

8. An Isosceles triangle has its equal side measuring 15.4 in. and its 3rd side measuring 23.9 in. What is its perimeter? 15.4*2+23.9 = 54.7 in.

9. A square measures 1.63 m. What is its perimeter? 1.63*4 = 6.52 m

10. A rhombus measures 8.06 ft. on a side. What is its perimeter? 8.06*4 = 32.24 ft.

11. A parallelogram measures 47.2 on one side and 36.8 on another. What is its perimeter? 47.2*2+36.8*2 = 168

12. A rectangle has dimensions 57.9 by 39.8 in. What is its perimeter?

2(57.9+39.8)= 195.4

Return to Problems


Slide28 l.jpg

13. Find the circumference of the circle whose radius is 14.3 cm.

Round to the nearest tenth. Ans. 2 (14.3) = 89.8

14. Find the circumference of the circle whose diameter is 8.4 in.

Round to the nearest tenth. Ans (8.4) =26.4

Find the perimeters of the indicated figures:

15.

6 ft.

6+7+11+18+12= 54 ft.

17.

7 ft.

12 ft.

28 cm.

11 ft.

58 + 12+

28+12+14+

12+16+12=

164cm

28+14+16=

58

12 cm.

18 ft.

60.8 ft.

14 cm.

16.

3/4 of a rectangle

plus 1/2 of a circle

46.0 ft.

16 cm

60.8*2+46+46*pi/2=239.9 ft.

12 cm

Return to same questions

Return to Next Problems


Slide29 l.jpg

18. 14.3 cm.

15.3 cm.

19.6 cm

This shape is a combination of a rectangle and two semi-circles.

The two semi-circles = one circle.

Top of Rectangle + bottom of rectangle + circumference of circle = perimeter

15.3 + 15.3 + 19.6 = 30.6 + 19.6 = 92.2 cm

End show

Back to beginning of questions


Slide30 l.jpg

Go to Geometry Part II 14.3 cm.

Similar Triangle


ad