work back from area to find height

How does Hero’s formula for triangle area also

make it easy for you to find the triangle’s height?

Solution

Using the other area formula, area - 1/2 base x height.

So, you can use Hero to find area and then divide by half the base to get height.

Hero’s formula and “1/2 base x height” work together

If you know three sides of a scalene triangle, you can use Hero’s formula to

find the area, and then use the formula you already know to find the height.

a

b

b

h

c

Semip

erimeter

Area = s (s-a) (s - b) (s - c)

s = a + b + c

2

Area = 1/2 b x h

h = 2 x area

b

Rearrange

Take y

our ar

ea value

f

rom her

e…

…and put i

t int

o the

other ar

ea f

ormula t

o

get the height.

198 Chapter 4

triangle properties

Q:

So do I actually ever need to do that gnarly three

Q:

Can I use Hero’s formula for isoceles and right triangles,

simultaneous equations thing? too?

A:No. It would work though, so if you ever can’t remember A:For a right triangle, 1/2 base x height is always easier as

Hero’s formula, it could get you out of a jam! But yeah—forget it. the two sides on the right angle give you base and height. For an

Sorry we did that to you.... isoceles triangle it’s up to you which you find easier.

Will the bargain screen still be visible to the

people at the back, 25 meters away?

So—can we use

the bargain

screen or what?

25m

28

31

30

T

he v

enue f

or

your gig

you are here 4 199

a perfect fit

Will the bargain screen still be visible to the

people at the back, 25 meters away?

28

31

30

Hero’s formula:

Area = s (s-a) (s - b) (s - c)

s = a + b + c

2

s = (31 + 30 + 28) / 2 = 44.5

Area = 44.5 (44.5-31) (44.5 - 30) (44.5 - 28)

= 44.5 x 13.5 x 14.5 x 16.5

= 143729 = 379.1 sq meters

Using conventional, 1/2 base x height, Height = 2 x area/base

Height = 2 x 379.1 / 30 = 25.27 m Perfect !

Do this bi

t firs

t then use i

t

in the

ar

ea f

ormul

a.

Combine tools from your toolbox to

get the answer you need.

Use the relationship between sides

and height to estimate angles.

There’s sometimes more than one

way to solve a problem—pick the

way that seems like the least amount

of work!

Draw sketches or graphs, or use your

hands if you’re stuck remembering

what those side-height-base

relationships are.

200 Chapter 4

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