Perimeter and AreaMultiplication 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.
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.

Shape Explorer  perimeter and area on a grid
Each of the links below provide additional interactive activiites.
Polygon/Circle 
P = Perimeter C = Circumference distance around the polygon/circle 
A = Area the surface inside the boundary( perimeter) 

P = b + c + d or P = s_{1} + s_{2} + s_{3} 
A = 1/2ab

P = b + c + d + e or P = s_{1} + s_{2} + s_{3} + s_{4} 
don't need to memorize the formula in junior high 


P = b_{1} + b_{2} + c + d or P = s_{1} + s_{2} + s_{3} + s_{4} 
A = 1/2ab_{1} + 1/2ab_{2}) simplifies to A = 1/2a(b_{1} + b_{2}) 

P = 2b + 2c 
A = bh 

P = 4s 
A = as 

P = 2l + 2w

A = lw 

A = s^{2} 

chevron 
P = 2c + 2d

don't need to memorize the area formulae in junior high 
kite 
P = 2c + 2d

don't need to memorize the area formulae in junior high 
pentagon = "five sides" 
P = ns

A = 0.5ans = 0.5aP 
Circumference is the distance around the circle.

C = Circumference C = pd 
A = Area A = p r^{2} 


Relationships:  1. For a square, nonsquare rectangle and circle with equal perimeter/circumference the relative area from largest to smallest is: 2. Increasing dimensions by a factor increases the perimeter by the same factor.

1. For a square, nonsquare rectangle and circle with equal areas the relative perimeter from largest to smallest is: 2. Increasing the dimensions by a factor increases the area by the square of the factor.

Polygon/Circle 
Perimeter/Circumference 
Study the surface area and volume for the prisms, pyramids, cylinder and cone provided.
Geometric Shape 
Surface Area B = area of the base P = perimeter of the base 
B = area of the base P = perimeter of the base 
prism (general)

SA = 2B + Ph  V = Bh 

SA = 2B + Ph
SA = 2(1/2ab) + (b + c + d)h SA = ab + (b + c + d)h 
V = Bh
V = 1/2 abh 

SA = 2B + Ph
SA = 2(lw) + (2l + 2w)h 
V = lwh 
Regular square prism

SA = 2B + Ph
SA = 2(s^{2}) + (4s)h 
V = Bh
V = s^{2}h 
regular pentagonal prism

SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(5)s + 5sh SA = 5as + 5sh 
V = Bh
V = 1/2ansh V = 1/2a(5)sh V = 5/2ash 
regular hexagonal prism

SA = 2B + Ph SA = 2(1/2ans) + nsh SA = 2(1/2a)(6)s + 6sh SA =6as + 6sh 
V = Bh
V = 1/2ansh V = 1/2a(6)sh V = 3ash 
cube

SA = 2B + Ph
SA = 2(s^{2}) + (4s)s = 6s^{2} 
V = Bh
V = s^{3} 
regular pyramid (general)

SA = B + n(1/2sl)
l = slant height 
V = 1/3Bh 
regular triangular pyramid

SA = B + n(1/2sl) SA = 1/2as + (3)(1/2sl) SA = 1/2as + 3/2sl
l = slant height 
V = 1/3Bh V = 1/3(1/2 ab)h V = 1/6 abh 
regular square pyramid

SA = B + n(1/2sl) SA = s^{2} + (4)(1/2sl) SA = s^{2} + 2sl
l = slant height 
V = 1/3Bh
V = 1/3(b^{2})h = 1/3b^{2}h 
regular pentagonal pyramid

SA = B + n(1/2sl) SA = 1/2a(5)s + (5)(1/2sl) SA = 5/2as + 5/2sl
l = slant height 
V = 1/3Bh
V = 1/3(1/2anb)h V = 1/6 anbh 
regular hexagonal pyramid

SA = B + n(1/2sl) SA = 1/2a(6)s + (6)(1/2sl) SA = 3as + 3sl
l = slant height 
V = 1/3Bh
V = 1/3(1/2anb)h V = 1/6 anbh 
cylinder

SA = 2B + Ph SA = 2(p r^{2}) + (2pr)h 
V = Bh V = p r^{2}h 
cone

V = 1/3 Bh V = 1/3pr^{2}h The volume of a cone is one third the volume of the corresponding cylinder. 

sphere r = radius of circle 
SA = 4pr^{2} 
V = 4/3pr^{3} 
Prism V = Bh 
Pyramid V = 1/3 Bh 
The volume of a pyramid is one third the volume of the corresponding prism. 
Cylinder V = Bh 
Cone V = 1/3Bh 
The volume of a cone is one third the volume of the corresponding cylinder. 