Geometry 8 ~ Mrs. Pohl Field School of Charlottesville (Fall-13)

Plane Areas and Perimeters III:

The plane shape, circle, has area and perimeter called "circumference." Here we study shapes having areas and perimeters related to circular geometry (and their representations in equation form).

1) Consult a resource (dictionary, text or internet), read the definitions and write them below. Learn the definitions these geometric entities:

a)  Point:


b)  Circle:


c)  Plane:


f)  Planar Shape:


d)  Area:


e)  Perimeter:


Each Case below gives a shape. Beside each shape write an equation for the area as
   "A =  ..."    and perimeter as   "P = ..."   Use the notations given.

2) Square

a) Area:

b) Perimeter:

3) Rectangle

a) Area:

b) Perimeter:

Area is easy to obtain. Perimeter
requires Theorem of Pythagoras.

4) Triangle

a) Area:

b) Perimeter:









That written above is a nice beginning. It leads, along a meaningful path, to valuable geometry. I can write this quickly if you want to use it. Or you can use it as review. Think about this plan ~ how to do with your text. All what I have for your needs needs clean-up only. (which I am doing anyway).

1) f) Planar Shape:   Mimi... you look up shape. Shape is an "abstraction". So what then is an abstraction?

2) square: A = L x L... easy

3) ... easy again

4) is more interesting than it seems. How do we know area4? We SEE it to be 1/2 of area of 2). The "1/2" is seen by vision. We use symmetry. Symmetry is wicked geometry (out of hell)

Also with 4)... the perimiter is two straight legs then one needs the Theorem of Pythagoras for the diagonal length. The second page I send shows how Pythagoras proved that diagonal length of a right triangle using areas of squares and triangles (we just did). The www has MANY other geometric proofs. Maybe ask them to find some.

Please consult a dictionary for terms I put in red.