Screencast Animated Lectures.

Javier Soto

6. GEOMETRY

Shapes

Triangles• 3 types:

Triangles: Pythagorean Relationship!• Lets look into what “Pythagorean Relationship” means:

• RIGHT Triangle. We can find missing side by following this formula!• A and B are the shorter sides. C is ALWAYS the longest side.

Example: Pythagorean Theorem• (Insert example from book)

Checklist for TRIANGLES:

THE FORMULA CHART IS YOUR FRIEND!

The formula chart is here to help you!

Look at the formula chart as DIRECTIONS on how to get the answer of what the math test is asking you for.

Looking for the AREA?

PERIMETER?

SURFACE AREA or VOLUME?

Things to know before diving into geometry

3. The little 2 on top,

1. Two letters together ALWAYS means MULTIPLICATION.• For example: A = lw means “AREA EQUALS LENGTH TIMES WIDTH”.

2. Look at the formula as DIRECTIONS to solve a problem.• For example: A = lw • Translate this into “in order to get the AREA, we must get the

LENGTH and MULTIPLY it by the WIDTH.

means that you have to get the number on one SIDE of the square and multiply it by itself.

such as in the FORMULA for the area of a square

2

A letter and A number together ALSO always means MULTIPLICATION. For example: 2L + 2w means “2 times the length plus 2 times the width.“

How to find the AREA of ANY shape:1. Identify the shape.• Is it a square? Triangle? Rectangle?

2. Look for the formula in the formula chart (insert arrow pointing to formula chart picture)

3. Plug in the numbers into the formula and solve.

PROBLEM SOLVED!

Area of a square:

A = S2FORMULA

Area“is” or “equals to”

Side

times itself

So, in order to get the AREA of this shape,

we have to multiply the SIDE, 2, by itself, 2.

22

2×2 =4

OR

=4

2

With a side measuring 2 feet.

4

Area:

A stands for AREA S stands for SIDE (as in, the number on the SIDE of a figure, usually a square)

l stands for LENGTHw stands for WIDTH

b stands for BASE (as in, the number on the BOTTOM of a figure, usually a triangle.

h stands for HEIGHT

What do these letters mean?

It’s all about plugging in the numbers!

What is the area of this rectangle?

4

2

A = lwArea

“is” or “equals to”

length width

Remember: two letters together means that those two numbers are being multiplied.

So, the AREA of this rectangle IS LENGTH (l) times the WIDTH (w). A=

So A = 8

8

A rectangle has a length of 4 centimeters by a width of 2 centimeters.

FORMULA:

x4 2, 4 x2 = 8,

How to find the PERIMETER of ANY shape (except for circles):• Just add all the sides of the shape!

Perimeter:

Just add all sides!

3

5

2

3

4

5

3+3+3+3=12

2+5+2+5=14 3+4+5=12

The measurement AROUND the shapes.

ALL sides in a SQUARE measure the same:

Opposite sides in a rectangle measure the same:

3

3

3If this side measures 3…

So does this side!

And these sides!

5

2

Perimeter:

Perimeter:

Perimeter:

Checklist for AREA & PERIMETER:

Circles• Stuff you have to know about circles:• AREA

• It is possible to find the “Area” of a circle, but the formula used to find it is a bit weird, or different: A = d(pi)

• IT’S NOT CALLED PERIMETER. IT’S CALLED CIRCUMFERENCE.• The perimeter, or the distance around a circle, is called the CIRCUMFERENCE. You also

have to use a weird formula in order to find it: A = pi x radius x radius• DIAMETER

• The distance measuring from one end of the circle to the opposite end is called the DIAMETER.

• RADIUS• HALF of the DIAMETER, is called the RADIUS.

Circles: Diameter and Radius.

Circles: Area• How to find the area of a circle:

Circles: Example 2 – Area

Circles: Circumference• How to find the CIRCUMFERENCE of a circle:

Circles: Example 1 – Circumference

Circles: Checklist

Surface Area

- Like area, but of 3D shapes

Surface Area and Volume