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Head First 2D Geometry by Dawn Griffiths, Stray

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Jus
t try
drawing a
triangle tha
t
br
eak
s this
rule!
regular polygons
You’ve found the formula for the area of an equilateral triangle
Recognizing special shapes is a great shortcut. Being able to spot
that a quadrilateral is a square, or that a triangle is an equilateral
triangle can save you a lot of work by letting you use extra tools
and formulas which apply to that special shape specifically.
Any old triangle Equilateral triangle
Sides
Angles
Area
Are all 60º
Add up to 180º
1/2 base × height
= 3 t
2
or Hero’s formula
4
Longest must be shorter than
other two sides added together
Are equal lengths
Use your new equilateral triangle area formula to find the butt
count of the triangular-shaped hot tub.
you are here 4 293
sharpen solution
Use your new equilateral triangle area formula to find the butt-
count of the triangular shaped hot tub.
3t
2
4
3t
2
4
Area =
Perimeter = 3t
= 3 x 3.72
= 11.17m
Butts = 11.17 = 22.3 butts
0.5
6 =
24 = t
2
3
3.72m = t
Length of
each side
Q:
Why bother learning another
formula? Won’t I be covered if I just
know Hero’s formula and the “1/2 base
× height” version?
A:Any time you use Hero’s formula
to work on a equilateral triangle you’re
gonna wind up doing all the math we just
did anyway. If you can learn the equilateral
triangle area formula then you won’t need to
do all that algebra again!
Q:
But what if I wanted to use “1/2
base × height.” I thought in geometry it
didn’t matter how you work stuff out, the
answer should be the same?
A:That’s true, and starting from 1/2
base × height, you’d have ended up with
the exact same formula. You just have to do
more work to get there. First you’d need to
use the Pythagorean Theorem to find the
sides in terms of the height, and then you’d
need to do some simultaneous equations to
put it all together. It would definitely work but
there’s a lot more to go wrong.
Q:
OK, so this formula only works
for equilateral triangles? What about
triangles that are nearly equilateral?
A:You could use it to approximate area
for a triangle with sides of similar length, but
it wouldn’t be accurate. It’s a good way to
check your answer in an exam though. Pick
the middle side length, work the equilateral
triangle area formula and it should come out
in the same ball park. If your two answers
are 9 and 10, you’re all good; if they’re 9
and 50, you know you need to check your
work.
294 Chapter 7
Frank
Jill
Joe
regular polygons
Dude, what did you
say the circle tub
butt-count was again?
Jill: Uh, I think it was like 19 point something.
Frank: No, that’s the square isn’t it?
Jill: Oh, yeah. Sorry. It’s on this other piece of paper.
Frank: And did you keep track of what the
dimensions were for the carpenters?
Joe: Yeah, well, uh, not exactly, but I did scribble it
down in my notes somewhere so I must have it.…
Hmm. This is getting messy fast. Do you think there’s a more
efficient way to keep track of the calculations for each hot tub?
you are here 4 295

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