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
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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
Objective 6.10 is really in three sections. Here is an overview.Sections A and B and pi (π) 3.14 (we do this after Winter Break)area of circles A =πr² circumference of circles C = πdSection C (Before Winter Break)Area of squares A= lw or A= s² because squares have congruent sidesPerimeter of squares P= 4s or P= S+S+S+SP= 4(3) or 3+3+3+3 P= 12 inArea of rectangles A= lwA= 7 • 2 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 bhor A=b•h÷2 A= ½ • 4 •3 A= .5•4•3 A= 6 inches squaredbecause triangles are ½ a square or rectangle Perimeter of triangles P= s+s+s P= 2 + 3 + 4 P= 9 inchesSection D (after Winter Break)Volume of a rectangular prism V = lwh Surface Area of a rectangular prism S.A. = 2lw + 2lh + 2wh
A= 3² or A= 3 x 3 = 9 square inches
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 = lw). 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.
Area of squares A= lw or A= s² because squares have congruent sidesPerimeter of squares P= 4s or P= S+S+S+S
Area of rectangles A= lwPerimeter of rectangles p = 2l + 2w or P=
Area of triangles A=½ bhor A=b•h÷2 because triangles are ½ a square or rectangle Perimeter of triangles P= s+s+s
pg 6.10c 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.
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
Or determine the
new length and
width and then
A=8 x 4
A= 32 ft²
32 x 3= 96 ft²
A= 18 • 12
A= 216 cm²
A= 12 x 8
A= 96 ft²
A= 336 ft²
Math Word Problems
Area and Perimeter
3 and 4 sided Polygons
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. 64b. 32c. 4d. 768
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 inchesb. 40 inchesc. 30 inchesd. There is not enough information to know.
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. 126b. 378c. 13d. 42
7. What is the area of triangle RST?
5 in 13 in
S 12 in T
B- 10 inches
15. I am covering a triangular shaped slice of pie with whipped cream. How much whipped will cover the pie?
b= 4 inches
Holiday HouseUse the figuring box to answer each questionWhen you are finished answering the questions, you may decorate your house for the holidays!
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.
6.10 a and bArea and Circumference of Circleshttp://www.brainpop.com/math/numbersandoperations/pi/http://www.brainpop.com/math/geometryandmeasurement/circles/
Pg 6.10 a and b Directions
DR your circle
If Radius given, double for diameter
If Diameter given, halve for radius
Determine what is being asked for,
AREA or CIRCUMFERENCE
3. Write the formula and take one step at a time
A= πx 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 25 C= 31.4 in
A= 328.5 in ²
6.10 a and b vocabulary pg 62
An inexact result adequate for a given purpose
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.
The distance around the outside of a circle (like perimeter) distance is a little over 3 times the diameter
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
The distance from the center of the circle to any point on the circle (half diameter)
The distance across a circle through the center (double radius)
Pg Practice Circumference
Practice Area 6.10 a and b pg
Pg ____ 6.10 d Examples:
Surface Area- (measured in square units)
Write this first
l = 8 in.
w = 12 in.
h = 2 in.
6.10 d pg.
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.
Surface area - (cover) The sum of the areas of all the surfaces (faces) of a three-dimensional figure . Answer is squared.
h= 2 in
SA = 2lw + 2lh + 2wh
SA = 2(8)(12) + 2(8)(2) + 2(12)(2)
SA = 2(96) + 2(16) + 2(24)
SA = 192 + 32 + 48
SA = 272 inches²
Volume (measured in cubic units)
Write this first
l = 8 in.
w = 12 in.
h = 2 in.
Pg____ 6.10 d Practice
Determine the Surface Area for each Rectangular Prism
6.10 d Practice pg______
Determine the Volume for each Rectangular Prism