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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