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Grade 8:  The Learning Equation Math

32.03 Area and Perimeter: Quadrilaterals and Circles

3icon.gif (4368 bytes)

3D Objects & 2D Shapes

Refresher pp 58-59

Learning Outcomes:

The student will:

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.

 

 

Try this applet to calculate the perimeter (distance around the shape) and area (number of squares in the shape) before studying the perimeter and area formulae:

Shape Explorer - perimeter and area on a grid

Interactive sums

 

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, Polygons, and Symmetry

Interactive sums - Areas and Volume

Lesson on Perimeter of Polygons

Lesson on Area of Rectangles

Lesson on Area of Parallelograms

Lesson on Area of Triangles

Lesson on Area of Trapezoids

Lesson on Area of a Circle

Circle Measurement

Area Flashcards

Constant Perimeter and Area(Rectangles)

Circumference

 

Grade 9 - Lesson 31.08

Key Terms:

area, quadrilateral, circumference, p, radius, opposite sides, parallel, right angle, base, height, parallelogram, rhombus, trapezoid, circumference, radius, diameter

Prerequisite Skills:

Powers and Exponents:   Grade 7 Lesson 11.01

Order of Operations:   Grade 7 Lesson 12.03

Circle Measurement:   Grade 7 Lesson 31.01

 

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Comments to:  Jim Reed
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