Area+Perimeter+Volume

**Multiplication Tables:** the product of two numbers can be represented by the area of a rectangle where the factors are represented as the dimensions of the rectangle. Notice each square in the area grid is a unit square.
 * ==Perimeter and Area ==
 * Area of a rectangle** is represented by a grid of unit squares. Perimeter is the distance around the outside rectangle.
 * Area of a square** is represented by a grid of unit squares. Perimeter is the distance around the outside square.
 * Area of a parallelogram** is represented by a grid of unit squares. Perimeter is the distance around outside of the parallelogram.


 * Area of a rhombus** is represented by a grid of unit squares. Perimeter is the distance around outside of the rhombus.


 * Area of Triangles** is represented by a grid of unit squares. Perimeter is the distance around outside of the triangle.


 * Area of Trapezoids** is represented by a grid of unit squares. Perimeter is the distance around outside of the trapezoid.

|| for more help help click here Maximize Area Interactive sums
 * Shape Explorer** - perimeter and area on a grid
 * Minimize Perimeter**

**Each of the links below provide additional interactive activiites.** || ||  **the surface inside the boundary( perimeter)** || P = b + c + d or P = s1 + s2 + s3 || A = 1/2ab **Note:** The area of the triangle is half the area of the corresponding parallelogram/rectangle. || P = b + c + d + e or P = s1 + s2 + s3 + s4 || don't need to memorize the formula in junior high enrichment || P = b1 + b2 + c + d or P = s1 + s2 + s3 + s4 || A = 1/2ab1 + 1/2ab2) simplifies to A = 1/2a(b1 + b2) || P = 2b + 2c || A = bh || P = 4s || A = as || P = 2l + 2w || A = lw || P = 4s || A = s2 || P = 2c + 2d
 * Polygon/Circle**
 * Polygon/Circle**
 * P = P**erimeter
 * C = C**ircumference
 * distance around the polygon/circle**
 * A = Area **
 * **triangle **
 * **a** = altitude
 * **b** = base || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/triangle_perimeter.gif width="130" height="110"]]
 * quadrilateral || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/quadrilateral_peri.gif width="130" height="110"]]
 * **trapezoid **
 * **a** = altitude
 * **b** = base || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/trapezoid_peri.gif width="130" height="110"]]
 * **parallelogram **
 * **a** = altitude
 * **b** = base || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/parallelogram_perimeter.gif width="130" height="110"]]
 * rhombus
 * **a** = altitude
 * **s** = side length || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/rhombus_perimeter.gif width="130" height="110"]]
 * **rectangle **
 * **l** = length
 * **w** = width ||
 * **square **
 * **s** = side length || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/square_perimeter.gif width="130" height="100"]]
 * chevron || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/cheveron.gif width="130" height="110"]]

|| don't need to memorize the area formula in junior high || P = 2c + 2d
 * kite || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/kite_peri.gif width="130" height="110"]]

|| don't need to memorize the area formulae in junior high enrichment || pentagon = "five sides" hexatagon = "six sides" heptaagon = "seven sides" octaagon = "eight sides" nonagon = "nine sides" decagon = "ten sides" || P = ns || A = 0.5ans = 0.5aP ||
 * **regular polygon **
 * **a** = apothem length
 * **s** = side length
 * **n** = #sides
 * **circle **
 * **circle **

Circumference is the distance around the circle. C = Circumference
 * **r** = radius of circle
 * **d** = diameter of circle ||

C = p d || A = Area

A = p r2 || || 1. For a square, non-square rectangle and circle with equal perimeter/circumference the relative area from largest to smallest is: circle, square, rectangle
 * **Relationships:** || **

2. Increasing dimensions by a factor increases the perimeter by the same factor.

tripling the dimensions triples the perimeter ** || 1. For a square, non-square rectangle and circle with equal areas the relative perimeter from largest to smallest is:
 * rectangle, square, circle

2. Increasing the dimensions by a factor increases the area by the square of the factor. tripling the dimensions increases the area by a factor of 9 (32). || || || <span class="wiki_link_ext">Area ||
 * Polygon/Circle**
 * Polygon/Circle**
 * Perimeter/Circumference**

 **B** = area of the **b**ase **B** = area of the **b**ase SA = 2(1/2ab) + (b + c + d)h SA = ab + (b + c + d)h || V = Bh V = 1/2 abh || SA = 2(lw) + (2l + 2w)h || V = lwh || SA = 2(s2) + (4s)h || V = Bh V = s2h || SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(5)s + 5sh SA = 5as + 5sh
 * **Geometric Shape** || **Surface Area**
 * P** = **p**erimeter of the base || **<span class="wiki_link_ext">Volume **
 * P** = **p**erimeter of the base ||
 * prism (general)
 * **B** = area of base
 * **P** = perimeter of base
 * **h**=height= || SA 2B + Ph || V = Bh ||
 * <span class="wiki_link_ext">triangular prism
 * **a** = altitude
 * **b** = base
 * **h**=#height= || SA 2B + Ph
 * <span class="wiki_link_ext">rectangular prism
 * **l** = length
 * **w** = width
 * **h**=height= || SA 2B + Ph
 * Regular square prism
 * **s** = side length
 * **h**=height= || SA 2B + Ph
 * regular pentagonal prism
 * **a** = apothem length
 * **s** = side length
 * **n** = #sides
 * **h** = height ||

|| V = Bh V = 1/2ansh V = 1/2a(5)sh V = 5/2ash || SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(6)s + 6sh SA =6 as + 6sh
 * regular hexagonal prism
 * **a** = apothem length
 * **s** = side length
 * **n** = #sides
 * **h** = height ||

|| V = Bh V = 1/2ansh V = 1/2a(6)sh V = 3ash || SA = 2(s2) + (4s)s = 6s2 || V = Bh V = s3 || //l// = slant height || V = 1/3Bh || SA = 1/2as + (3)(1/2s//l//) SA = 1/2as + 3/2s//l//
 * cube
 * **s**=side length= || SA 2B + Ph
 * regular pyramid (general)
 * **B** = area of base
 * **s** = side length
 * **//l//**=slant height= || SA B + n(1/2s//l//)
 * regular triangular pyramid
 * **a** = apothem length
 * **s** = side length
 * **n** = #sides
 * //**l**// = slant height
 * **h**=height= || SA B + n(1/2s//l//)

//l// = slant height || V = 1/3Bh V = 1/3(1/2 ab)h V = 1/6 abh

|| SA = s2 + (4)(1/2s//l//) SA = s2 + 2s//l// //l// = slant height || V = 1/3Bh V = 1/3(b2)h = 1/3b2h || SA = 1/2a(5)s + (5)(1/2s//l//) SA = 5/2as + 5/2s//l// //l// = slant height || V = 1/3Bh V = 1/3(1/2anb)h V = 1/6 anbh || SA = 1/2a(6)s + (6)(1/2s//l//) SA = 3as + 3s//l// //l// = slant height || V = 1/3Bh V = 1/3(1/2anb)h V = 1/6 anbh || SA = 2( p r2) + (2 p r)h
 * regular square pyramid
 * **s** = side length
 * **n** = #sides
 * //**l**// = slant height
 * **h**=height= || SA B + n(1/2s//l//)
 * regular pentagonal pyramid
 * **a** = apothem length
 * **s** = side length
 * **n** = #sides
 * //**l**// = slant height
 * **h**=height= || SA B + n(1/2s//l//)
 * regular hexagonal pyramid
 * **a** = apothem length
 * **s** = side length
 * **n** = #sides
 * //**l**// = slant height
 * **h**=height= || SA B + n(1/2s//l//)
 * cylinder
 * **B** = area of base
 * **P** = perimeter of base
 * **r** = radius of circle
 * **h**=height= || SA 2B + Ph

|| V = Bh V = p r2h

||
 * cone
 * **B** = area of base
 * **r** = radius of circle
 * **h** = height || [[image:http://staff.argyll.epsb.ca/jreed/math9/strand3/images/cone_sml.gif width="149" height="90" align="center" caption="cone_sml.png (34352 bytes)"]]

<span class="wiki_link_ext">Explanation || V = 1/3 Bh V = 1/3 p r2h

The volume of a cone is one third the volume of the corresponding cylinder. || || SA 4 p r2
 * sphere
 * r**=radius of circle=

|| V = 4/3 p r3

||

V = **B**h || **Pyramid** V = 1/3 **B**h || The volume of a pyramid is one third the volume of the corresponding prism. || V = **B**h || **Cone** V = 1/3Bh || The volume of a cone is one third the volume of the corresponding cylinder. ||
 * **Prism**
 * **Cylinder**

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