1. 6.10
The student will
Define pi ( π) as a ratio of the circumference of a circle to its diameter
b) Solve practical problems involving circumference and area of a circle, given the diameter or radius
c) Solve practical problems involving area and perimeter
d) Describe and determine the volume and surface area of a rectangular prism
     

2. Brain Pop Area of Polygons

3. A= 3² or A= 3 x 3 = 9 square inches
Objective 6.10 is really in three sections. Here is an overview. Sections A and B and pi (π) (we do this after Winter Break) area of circles A =πr² circumference of circles C = πd Section C (Before Winter Break) Area of squares A= lw or A= s² because squares have congruent sides Perimeter of squares P= 4s or P= S+S+S+S P= 4(3) or P= 12 in Area of rectangles A= lw A= 7 • A = 14 square inches Perimeter of rectangles p = 2l + 2w or P= S+S+S+S P= 2(7) + 2(2) P= 14+4= 18 in Area of triangles A=½ bh or A=b•h÷ A= ½ • 4 • A= .5•4•3 A= 6 inches squared because triangles are ½ a square or rectangle Perimeter of triangles P= s+s+s P= P= 9 inches Section D (after Winter Break) Volume of a rectangular prism V = lwh Surface Area of a rectangular prism S.A. = 2lw + 2lh + 2wh
7 in
2 in
h=3 in
b=4 in
2 in
4 in
3 in

4. 8 in 10 in 6 in A=½ bh P= s+s+s A= .5•6•7 A= 15 in² Pg _____ 6.10c
Directions- MA and PA….multiply area and perimeter add.
Draw a picture of the situation to determine if it is area or perimeter. Label the measurements. Write formulas and solve
Key words-
Area- cover, carpet, grass, mow, an area, paint, tile
Perimeter- fence, trim, border, enclose, hem, edge, around
Examples
SQUARE
A= S² or A= lw P= 4s or P= s+s+s+s
A= 8 ² A=8• P= 4(8) P=
A= 64 in² A= 64 in² P= 32 in P= 32 in
RECTANGLE
A=lw P= 2l + 2w
A= 10 • P = 2(10) + 2(6) Or for perimeter just add all the sides
A= 60 in² P=
P= 32 inches
TRIANGLE (remember that ½ is .5)
A=½ bh P= s+s+s
A= .5•6•7
A= 15 in²
6.10c Vocabulary pg____
Polygon –A polygon is a simple, closed, two-dimensional figure formed by three or more sides.
Area – It is the product of the length and the width (A = l  w). The area of a triangle is one half of the measure of the base times the height:
Perimeter –The perimeter of a polygon is the measure of the distance around the polygon.
Length(l) - The measurement of the extent of something along its greatest dimension.
Width(w) - The measurement of the extent of something from side to side.
Base(b) – Bases are the top and bottom faces of a three-dimensional object.
Height(h) –The shortest distance from the base of a parallelogram to its opposite side.
FORMULAS
Draw & Key Word Formula and Work Answer
8 in
10 in
6 in
Area of squares A= lw or A= s² because squares have congruent sides Perimeter of squares P= 4s or P= S+S+S+S
Area of rectangles A= lw Perimeter of rectangles p = 2l + 2w or P=
Area of triangles A=½ bh or A=b•h÷2 because triangles are ½ a square or rectangle Perimeter of triangles P= s+s+s
H=7 in
b=6 in

5. 2. Sew a trim on a table cloth that is 6 ft x 4 ft.
6.10c Practice pg-
Table cloth covers 6ft x 4 ft table.
2. Sew a trim on a table cloth that is 6 ft x 4 ft.
3. Paint a wall that is 10 ft x 8 ft.
 4. How much frosting for a triangular shaped cake that’s base 5 inches and height is 2 inches
5. Sewing a ribbon around a triangle with a base of 8 inches and two sides each 7 inches.
pg c Practice
Find the area of a 13cm x 9cm rectangle.
Find the perimeter of a 20m x 10m rectangle.
Find the area of a square with a 5 inch side
Find the perimeter of a square with a 6 ft side
Find the area of a triangle with a 7 mm height and a 8 mm base
Find the perimeter of a triangle with the sides 1in, 2in, and 3 inch.
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer
Draw & Key Word Formula and Work Answer

6. 6.10c pg
You will be asked to determine area with partial information. Draw the figures as shown.
Label each square, then figure out the total length and width for each side.
You plan to push three tables together for a party. For one table, the length is 8 ft and its width is 4 ft. All three tables are the same size. What is the total area once you push all three tables together?
You can solve by
figuring one
table’s area
and then
multiplying
by three
Or determine the
new length and
width and then
solve area
18 cm
8 ft
4 ft
3 cm
A=lw
A=8 x 4
A= 32 ft²
32 ft
32ft
32 x 3= 96 ft² 3 3 3 3 3
12 cm 3 3 3
21 ft
A= lw
A= 18 • 12
A= 216 cm²
8 ft
4 ft
A= lw
A= 12 x 8
A= 96 ft²
7 ft
4 ft 7 7
16 ft 4 4
A=lw
A=21•16
A= 336 ft² 4

7. Area ______________Perimeter______ Area ____________Perimeter________
1) Rectangle 3ft x 7ft
5) Square 4 cm side
Area ______________Perimeter______
 Area ____________Perimeter________
2) Triangle 14 cm base and 20 cm height
6) Rectangle 5 yards x 7 yards
Area _____________Perimeter_______
Area ___________Perimeter___________
  3) Rectangle-
7) Triangle 14 foot base and 15 foot height
Each little square is
4 cm x 4cm
Area _____________
Area ____________Perimeter__________
4) Triangle 5 inch base and 13 inch height
8) Triangle 4.2 inch base and 14 inch height
Area ____________Perimeter___________
Area ___________Perimeter_________
4 cm
4 cm

8. 6.10c
Math Word Problems
Area and Perimeter of
3 and 4 sided Polygons

9. 1. Samantha owns a ranch that covers 48 square miles
1. Samantha owns a ranch that covers 48 square miles. She will plant wheat on all the land except for 16 square miles. Samantha will plant wheat on __________ square miles of land.
a. 64 b. 32 c. 4 d. 768
Draw & Key Word Formula and Work Answer

10. 2. A rectangle is 5 inches wide
2. A rectangle is 5 inches wide. The area of the rectangle is 35 square inches. What is the perimeter of the rectangle?
a. 24 inches b. 40 inches c. 30 inches d. There is not enough information to know.
Draw & Key Word Formula and Work Answer

11. 3. John’s bedroom is exactly 18 feet by 21 feet
3. John’s bedroom is exactly 18 feet by 21 feet. He wants to get carpeting to cover the entire floor. How many square yards of carpeting does he need?
a. 126 b. 378 c. 13 d. 42
Draw & Key Word Formula and Work Answer

12. Key Word Formula and Work Answer

13. Draw & Key Word Formula and Work Answer

14. 7. What is the area of triangle RST? R
Draw & Key Word Formula and Work Answer
7. What is the area of triangle RST? R
5 in in
S in T

15. 8. What is the area of the large rectangle shown if each small square is 2 inches wide and 2 inches long?

16. 10. Sam and Abby are covering their table with newspaper before beginning an art project. Their table is 48 inches by 60 inches. How many square inches of newspaper will they need?
Draw & Key Word Formula and Work Answer

17. 11. The brown tiles that the kids of KFMS walk on, border a hall that is 80 foot long on each side (there are two sides). How many feet of brown tile is that?
Draw & Key Word Formula and Work Answer

18. 12. June is painting her front door red. Her door is 8 ft by 3 ft
12. June is painting her front door red. Her door is 8 ft by 3 ft. How any feet of paint will she need to cover the door?
Draw & Key Word Formula and Work Answer

19. 13. A picture measures 5 inches by 5 inches
13. A picture measures 5 inches by 5 inches. How much wood is needed to frame the
picture?
Draw & Key Word Formula and Work Answer

20. What is the area of the triangle?
H-6 inches
B- 10 inches
Draw & Key Word Formula and Work Answer

21. 15. I am covering a triangular shaped slice of pie with whipped cream
15. I am covering a triangular shaped slice of pie with whipped cream. How much whipped will cover the pie?
b= 4 inches
H=6 inches
Draw & Key Word Formula and Work Answer

22. Holiday House Use the figuring box to answer each question When you are finished answering the questions, you may decorate your house for the holidays!
Draw & Key Word Formula and Work Answer

23. Answer the questions, then glue your answers on the back of construction paper.
Next decorate your house. Finally, the outside fits
over the inside on the front of your construction paper.

24. Name_________________ 6.10 c Date___________
It is time to decorate and get the house ready for holiday company!
1. The kitchen floor needs to be retiled before every one comes to visit for the holidays. How many square feet of tile will you need to buy?
2. The living room needs new carpet before the company arrives. How much carpet will you need to buy?
3. You are planning to cover the front door with festive red foil paper. The door is 7 feet tall and 3 feet wide. How many square feet of foil paper will you need to cover the door?
4. You are going to make a holiday tablecloth for your 3’ X 4’ table. How many square feet of material will you need to buy?
5. You decided to add a holly trim to the edge of the tablecloth mentioned in question 4. How much holly will you need to buy?
6. You are going to enclose the front porch with holiday lights. The porch is a rectangle that is 30 feet long and 6 feet wide. How many feet of lights will you need?
7. You need to cover the couch cushions with a blanket because your brother is coming to visit for the holidays and has three BIG dogs he is bringing with him. What a mess they make! Your couch is 6 feet long and two feet wide. How much area does the blanket need to cover?
8. Your flower garden is 10 feet by 3 feet and you would like to put a really neat lighted snowman border around it. How many feet of lighted snowmen will you need to buy?
9. Next, the lawn needs to be mowed before everyone gets to your house. Your yard is 50’ X 70’. How many square feet will you have to mow?
10. Finally, the last yard project is putting a fence up around your 50’ X 70’ yard to keep your brother’s three big messy dogs out of the street and chasing cars. How many feet of fencing will you need to buy to fence in your yard to keep those dogs out of trouble?

25. 6. 10 a and b Area and Circumference of Circles http://www. brainpop

26. Ex- Pg 6.10 a and b Directions DR your circle
If Radius given, double for diameter
If Diameter given, halve for radius
Ex-
Determine what is being asked for,
AREA or CIRCUMFERENCE
Write the formula and take one step at a time
Area Circumference
A= π x r x r C= π x d
A= πr² C= πd
A= 3.14 x 5² C= 3.14 x 10
A= 3.14 x C= 31.4 in
A= in ²
6.10 a and b vocabulary pg 62
approximation
An inexact result adequate for a given purpose
 ratio
A comparison of two numbers by division. Example: The ratio 2 to 3 can be expressed as 2 out of 3, 2:3, or 2/3.
circumference
The distance around the outside of a circle (like perimeter) distance is a little over 3 times the diameter    pi
The ratio of the circumference of a circle to the diameter of a circle; equal to the fraction 22/7; often written as the approximation 3.14
 radius
The distance from the center of the circle to any point on the circle (half diameter)
diameter
The distance across a circle through the center (double radius)
D- 10
R-5
D- 10
R-5
5 in
10 in

27. Pg Practice Circumference
Practice Area a and b pg

28. 6. 10 d Volume and Surface Area of a Rectangular Prism http://www

29. V=lwh SA=2lw+2lh+2wh Pg ____ 6.10 d Examples: 6.10 d pg. w=12 in
Surface Area- (measured in square units)
SA=2lw+2lh+2wh
Write this first
l = 8 in.
w = 12 in.
h = 2 in.
6.10 d pg.
Rectangular Prism
Volume and Surface area
Net - An arrangement of
two-dimensional figures that
can be folded to form a polyhedron
Rectangular prism - A solid figure that has two parallel and congruent bases that are rectangles (a box)
Volume - (fill) The number of cubic units needed to fill the space occupied by a solid. Answer is cubed.
V=lwh
Surface area - (cover) The sum of the areas of all the surfaces (faces) of a three-dimensional figure . Answer is squared.
SA=2lw+2lh+2wh
w=12 in
h= 2 in
l=8 in
height
length
width
SA = 2lw + 2lh + 2wh
SA = 2(8)(12) + 2(8)(2) + 2(12)(2)
SA = 2(96) + 2(16) + 2(24)
SA =
SA = 272 inches²
Volume (measured in cubic units)
V=lwh
Write this first
l = 8 in.
w = 12 in.
h = 2 in.
V=lwh
V=(8)(12)(2)
V=192 in³

30. Pg____ d Practice
Determine the Surface Area for each Rectangular Prism
6.10 d Practice pg______
Determine the Volume for each Rectangular Prism
12 in
5 in
4 in
12 in
5 in
4 in
3 in
5 in
7 in
3 in
5 in
7 in
3 in
4 in
10 in
3 in
4 in
10 in