Pythagoras 11'4 Surface Area 11'5 Volume, Mass, Temp

1
Pythagoras11.4 Surface Area11.5 Volume, Mass,
Temp
2
Let no one ignorant of Mathematics enter here.

• Plato

3
Given-Square-Length a
a
b
a
c
c
b
Are the triangles congruent?
b
c
c
a
What type of quadrilateral is formed by
connecting the points?
b
a
What is the area of the large square?
What is the area of the small square?
What is the area of all four triangles?


4
Area
a
b
(ab)2
a
c2
c
c
b
c
b
c
a
b
a
What is the area of the large square?
What is the area of the small square?
What is the area of all four triangles?


5
Commensurable/Incommensurable
Let Red be 4 feet
Let Purple be 6 feet
LCM 12
Are there any numbers, lengths, that are
incommensurable?
6
He is unworthy of the name of man who is ignorant
of the fact that the diagonal of a square is
incommensurable with its side.

• Plato

7
The diagonal of a square is incommensurable with
its side.
c
1
1
8
What is the length of a diagonal of a square that
has an area of 25ft2?
25 ft2
5 ft
5 ft
9
What is the length of a diagonal of a square that
has an area of 32ft2?
32 ft2
10
Special Triangle 30o 60o -90o
2
2
h
1
1
2
Why is it a 30-60-90 degree triangle?
11
What is the area of an equilateral triangle that
has a perimeter of 24 ft?
8
8
h
4
4
8
ft2