calculate area of garden - square meters

[minniehaha19]

how do I work out the total square meters of a triangular shaped garden? The sizes are: 30m x 23m x 27m

[Huderon]

If the 30m length was the hypotenuse it would be (23 x 27) divided by 2 - at least I'm pretty sure that the area of a triangle is half the area of the rectangle it fits into !

[heathfield]

Let S represent half the total of the sides added together (30+27+23)/2

Therefore S = 40

Calculate S x (S-30) x (S-27) x (S-23) = 88,400

Take the square root of 88,400 = 297.32

And that's the area in square metres

[olly8080]

just in case you didnt understand that here is the simple way imagine it to be square work out the sqM and divide by 2

[Peter Pedant]

Hi minnie-ho minnie!

just in case you are wondering why you have four ways of doing it: one and three are wrong because they have assumed that there is a right angle in the triangle.

Look out of your window: there isnt , is there ? In fact all the angle look almost the same as the sides are almost the same length.

Method 2 is called Hero's formula - looks pretty impressive
s(s-a)(s-b)...etc
and is the CORRECT one.


Method one - which wouldnt get you Maths O level
gives and answer 320.5 m2
and you will notice is wrong but not very wrong
it is correct within 10 %

OK for engineers who are all failed mathematicians anyway.

[mibn2cweus]

For any and all triangles having a right angle, the sum of the squares of the 2 shorter sides (adjacent to the right angle) equals the square of the longest and opposite side (the hypotenuse).

(23 X 23) + (27 X 27) = 1258
(30 X 30) = 900

Nope, not a right triangle, so apply "Heron's formula".

Not that it matters (wrong is wrong) but

( 23 X 27 ) / 2 = 310.5 "correct" with-in 5% . . .

Thanks to the maths skills of engineers, technicians not only have a job but someone to blame it on as well.


. . . and I concur with Peter Pedant, heathfield�s answer is correct!

[kwicky]

I notice that all the answers above are mathematical and not related to practicalities. I notice you say total square metres. Because of the shape of your garden there will be considerable overlap if you are trying to get fixed dimensional objects to fit inside the boundaries.

[minniehaha19]

Thanks to all of you for you answers. Great help! Needless to say, I'm wishing I HAD stuck in with maths! I wouldn't feel so darn stupid! :)

[bird_81]

Here's an easy website with diagrams showing various ways to solve.
http://www.mathgoodies.com/lessons/vol1/area_t riangle.html