Melody

To understand the volume and the surface area of 3D shapes it is essentual that you understand the area of 2D shapes first.

You see, to find the surface area of 3D shapes you just add up the areas of all the sides.

To find the volume of any prism you just find the area of the side that stays the same all the way through and then multiply it by the depth.    (some people call the depth the height, it doesn't matter what you call it, if you UNDERSTAND what you are doing then the different names will not confuse you.)

The bottom clip on this post covered volume of prisms.  

$$\\6*6=6^2\\
8*8=8^2\\
L*L=L^2\\$$

That is what squared means 

Hi MG

ALL THE SYMBOLS THAT I USE HAVE A PURPOSE.   

Do you mean this line

$$\mathbf{If\quad L^2=9\qquad then\; \; L=\sqrt{9} = 3cm}$$

rectangle

Area = Length*Breadth

A square is just a special rectangle where     length=  breadth    So

Area of a square = L*L

but L*L can be written as     $$L^2$$

So with the little rectangle 

$$\mathbf{If\quad L^2=9\qquad then\; \; L=\sqrt{9} = 3cm}$$

This is because the inverse of square is square root.

---------------

Isn't this area stuff a part of what you mean by shapes?

Here is a good post that might help you with negative numbers

Hi MG,

I decided I would persist with this today because you have length and area in your test tomorrow so it might help.

FIRST SQUARE

What I wanted you to say here is that the area of the first square is $$16cm^2$$    

DO NOT FORGET THE SQUARED UNITS.   This is very important because it is the number of SQUARES that fit inside the plane (flat) shape.

I asked for 2 reasons 

Reason 1):  There is 16 squares inside that shape.  Each square has a side length of 1cm.  

So there are 16     1cm squares.      That is   $$16cm^2$$

Reason 2:    A=L*L = 4*4 = $$16cm^2$$

SECOND SQUARE

The area of this square is $$9cm^2$$   I know that because I can COUNT the 9 squares AND because I am told.

The side length is 3cm     I know the side is 3 cm because i can see it on the picture.

I also know the side is 3cm because the area is   $$9cm^2$$    and area is  Length*length = $$L*L=L^2$$

 $$\mathbf{If\;\;\;\;L^2=9\qquad then\; \; L=\sqrt{9} = 3cm}$$

Hi Pyramid :)

You have not specified a base.

Just to make the illustration easier I will make it base 2

Lets look atsome values for    $$y=log_2x$$

$$\\log_28=3\qquad $because $8=2^3\qquad (8,3)\\\\
log_24=2\qquad $because $4=2^2\qquad (4,2)\\\\
log_22=1\qquad $because $2=2^1\qquad (2,1)\\\\
log_21=0\qquad $because $1=2^0\qquad (1,0)\\\\
log_2\frac{1}{2}=-1\qquad $because $\frac{1}{2}=2^{-1}\qquad (\frac{1}{2},-1)\\\\
log_2\frac{1}{4}=-2\qquad $because $\frac{1}{4}=2^{-2}\qquad (\frac{1}{4},-2)\\\\
log_2\frac{1}{8}=-4\qquad $because $\frac{1}{8}=2^{-3}\qquad (\frac{1}{8},-3)\\\\$$

Now I can plot these points and then draw the points joining them as accurately as I can.

Now I can estimate other outputs directly from the graph.

Here is the graph

@@ End of Day Wrap  Sat 13/6/15   Sydney, Australia Time   2:20am  (Really Sunday)   ♪ ♫

Hello all,

Great answers from Alan, Heureka, Civonamzuk, Dragonlance, Eloise1st, DarkBlaze347 and Radix.  Thanks all. 

mrs adam bought cinema tickets for 4 adult and SOME children. an adult ticket is £5 an children ticket is £4 mrs adam paid a total of £48 work out the number of child tickets bought by mrs adam

Adults tickets are 4*5=20 pounds

48 pounds - 20 pounds = 28 pounds  (this is the total cost of the children's tickets.)

28 divided by 4 = 7               (Edited: thanks Alan)

She took 7 children :)

Here is a video on perimeter and area that I think it might be really good for you to watch.Don't give up on it to easily. it only goes for 8.5 minutes and I think you might get a fair bit out of it.

If you are sure you understand ALL of this then we'll look at some harder ones.