Area and Perimeter

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Grade 9: The Learning Equation Math

31.08 Area and Perimeter

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Measurement

Refresher pp 72-3

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Prerequisite Skills:

Estimate and measure the effect on perimeter of changing one or more dimensions of a rectangle.

Relate perimeters and areas of rectangles.

Perimeter and Area Relationships
Shape	Equal Perimeters	Equal Areas
rectangle	rectangle will have the least area	rectangle will have the greatest perimeter.
square	will have a greater area than the rectangle	will have a perimeter less than rectangle
circle	circle with have the greatest area	circle will have the least perimeter.

Constant Perimeter and Area Rectangles

Estimate and calculate the areas of composite figures.

area, perimeter, rate of change, radius, circumference

Learning Outcomes:

The student will:

calculate areas and perimeters.

Perimeter and Area

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.

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

Maximize Area

Minimize Perimeter

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)
triangle a = altitude b = base	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.
quadrilateral	P = b + c + d + e or P = s₁ + s₂ + s₃ + s₄	don't need to memorize the formula in junior high enrichment
trapezoid a = altitude b = base	P = b₁ + b₂ + c + d or P = s₁ + s₂ + s₃ + s₄	A = 1/2ab₁ + 1/2ab₂) simplifies to A = 1/2a(b₁ + b₂)
parallelogram a = altitude b = base	P = 2b + 2c	A = bh
rhombus a = altitude s = side length	P = 4s	A = as
rectangle l = length w = width	P = 2l + 2w	A = lw
square s = side length	P = 4s	A = s²
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 enrichment
regular polygon a = apothem length s = side length n = #sides 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

circle Circumference is the distance around the circle. r = radius of circle d = diameter of circle	C = Circumference C = pd	A = Area A =p r²

Relationships:	1. For a square, non-square rectangle and circle with equal perimeter/circumference the relative area from largest to smallest is: circle, square, rectangle 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).
Polygon/Circle	Perimeter/Circumference	Area