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Head First 2D Geometry by Dawn Griffiths, Stray

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Y
ou might need to
use the Pythagorean
T
heor
em to find this.
triangle properties
The area of a triangle = 1/2 base x height
The area of a triangle is half the area of the bounding
rectangle you could draw around it. It’s usually written and
found using the formula “half of base times height.” The
Height
Base
base is any one of the sides, and the height is the length of
the altitude you could draw on that side to the opposite vertex
The height is
the length of
the a
ltitude
on the base.
Height
Base
T
he ar
ea of
the bounding
rec
tangle would
be base x height.
Base
So does this mean
we’re ready to
choose a venue?
(corner).
Height
you are here 4 163
choose your venue
Which venue gives you the most money to
spend on the festival (and split the profits)?
Don’t forget that you’ve got fencing costs.
Assume it’s a sellout and that each person
needs 2 square meters of area.
567982
admit one
rock festiv
al
$10.00
Fencing = $3885
Fencing = $3750
Fencing = $3420
90m
60m
Field A
80m
85m
85m
Field B
42m
33m
33m
60m
60m
Field C
164 Chapter 4
triangle properties
So—which venue do you choose?
you are here 4 165
you’ve found the best venue
Which venue gives you the most money to
spend on the festival (and split the profits!)?
Don’t forget that you’ve got fencing costs.
Assume it’s a sellout and that each person
needs 2 square meters of area.
567982
admit one
rock festiv
al
$10.00
A
Ar
ea of tr
iangle = 1/2 base x height
Area = 1/2 x 90 x 60
= 2700 sq meters
People = 2700 = 1350
2
Ticket money = 1350 x 10 = $13500
Cost of fencing = $3885
Remaining money = 13500 - 3885 = $9615
2 square meter
s
p
er person
$10 p
er ticket
W
orked out earli
er
Fencing = $3885
Fencing = $3750
Fencing = $3420
90m
60m
Field A
80m
85m
85m
Field B
42m
33m
33m
60m
60m
Field C
166 Chapter 4
F
or an isosceles
triangle the a
lti
tude
bisec
ts the base.
triangle properties
B
First we need to find the height, using the Pythagorean Theorem:
H
2
= 85
2
- 40
2
H = 7225 - 1600 = 5625 = 75m
Area = 1/2 x 80 x 75
= 3000 sq meters
People = 3000 = 1500
85
H
85
2
Ticket money = 1500 x 10 = $15000
Cost of fencing = $3750
Remaining money = 15000 - 3750 = $11250
40
40
C
This shape is like a rectangle with a triangle on
the top.
Area of the rectangle bit = 42 x 33 = 1386 sq meters
For the triangle we need to find the height—using the
33
Pythagorean Theorem:
H
2
= 60
2
- 21
2
60 60
H
21
21
42
H = 3600 - 441 = 3159 = 56.2m
Triangle Area = 1/2 x 42 x 56.2 = 1180 sq meters
Total Area = rectangle area + triangle area = 1386 + 1180 = 2566 sq meters
People = 2566 = 1283
2
Ticket money = 1283 x 10 = $12830
Cost of fencing = $3420
Remaining money = 12830 - 3420 = $9410
So—which venue do you choose?
Field B is the best!
you are here 4 167
33

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