Composite Areas

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Grade 8: The Learning Equation Math

32.05 Composite Areas

3icon.gif (4368 bytes)

3D Objects & 2D Shapes

Refresher pp 62-63

Learning Outcomes:

The student will:

estimate and calculate the area of composite figures.

Composite areas require knowledge of the area formulae.

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

Area of a trapezoid 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
triangle	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	P = b₁ + b₂ + c + d or P = s₁ + s₂ + s₃ + s₄	A = 1/2ab₁ + 1/2ab₂) simplifies to A = 1/2a(b₁ + b₂)
parallelogram	P = 2b + 2c	A = bh
rhombus	P = 4s	A = as
rectangle	P = 2l + 2w	A = lw
square	P = 4s	A = s²
chevron	don't need to memorize the perimeter/area formulae in junior high
kite	don't need to memorize the perimeter/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.	C = Circumference C = pd	A = Area A =p r²

Polygon/Circle	Perimeter/Circumference	Area