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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:

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

 

Key Terms:

area, composite, 2D figure, congruent, parallel, parallelogram, trapezoid

Prerequisite Skills:

Order of Operations:   Grade 7 Lesson 12.03

 Area and Perimeter: Quadrilaterals and Circles:  Grade 8 Lesson 22.03

 

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Comments to:  Jim Reed
Started September, 1998. Copyright 1999, 2000

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