1. The document provides information and examples about geometry concepts including triangles, the Pythagorean theorem, area, perimeter, circles, surface area, and volume. 2. It explains key terms like radius, diameter, circumference, and formulas for finding the area of squares, rectangles, triangles, and circles. 3. Step-by-step examples are given for using formulas to calculate the area of shapes and the circumference of circles.

1. Screencast Animated
Lectures.
Javier Soto

2. 6. GEOMETRY

3. Shapes

4. Triangles
• 3 types:

5. Triangles: Pythagorean Relationship!
• Lets look into what “Pythagorean Relationship” means:
• 𝐴2 + 𝐵2 = 𝐶2
• RIGHT Triangle. We can find missing side by following this formula!
• A and B are the shorter sides. C is ALWAYS the longest side.

6. Example: Pythagorean Theorem
• (Insert example from book)

7. Checklist for TRIANGLES:

8. THE FORMULA CHART IS YOUR FRIEND!

9. 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?

10. 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 𝐴 = 𝑆
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.“

11. 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!

12. Area of a square:
A = S2
FORMULA
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

13. Area:
Astands for AREA S stands for SIDE (as in, the number on
the SIDE of a figure, usually a square)
l stands for LENGTH
w 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?

14. 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 rectanglehas a length of 4 centimeters by a width of 2 centimeters.
FORMULA:
x4 2,
4 x2 = 8,

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

16. 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:

17. Checklist for AREA & PERIMETER:

18. 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.

19. Circles: Diameter and Radius.

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

21. Circles: Example 2 – Area

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

23. Circles: Example 1 – Circumference

24. Circles: Checklist

25. Surface Area
- Like area, but of 3D shapes

26. Surface Area and Volume