How Would I Work Out The Area Of This Trapezium?

[CharmingBasil8]

I am stuck on this question, if anyone could help that would mean a lot! Here it is https://assets.hegartymaths.com/areatrap3.png

[Atheist]

I think Tora^3 said "A=(a+b)/2*h"
Maybe he should have said "A=((a+b)/2)*h"
I wait to be shot down (but not by cuby, who isn't talking to me.)

[bobbinwales]

well to be fair I do remember from night school it now I seen it again... the way we was tought to remember it was its linked to a rectangle (width x height)- just for a trapezum do 'average' width x height

[ToraToraTora]

"Yes that was the method TTT first suggested.
But its not a formula that memorable for most of us or easy to understand why it works.... triangles and rectangles are easier to remember how to work out area's for " - yes bob the formula is what I said at first. I mistyped one of the 3 areas of the alternative method and corrected it later. pity some choose to ignore that.

[THECORBYLOON]

The area within a circle is pi × the square of the radius.

The formula, πr^2 can be derived for those interested enough in knowing why but for most folk, only the formula is needed not the reason.

[ZebuSanctuary]

CharmingBazil, Listen Carefully:

A trapezium is any quadrilateral (a shape with 4 sides) where two of the sides are parallel to one another. Thus the link depicts a trapezium. Once identified, the area of ALL trapeziums can be determined by the following formula:

Area = (a + b) * h / 2

where a and b are the lengths of the parallel sides and h is the vertical height between the parallel sides. The * and / are the multiplication and division signs respectively.

Thus Area = (19 + 4) * 5 / 2

Area = 23 * 5 / 2

Area = 115 / 2

Answer Area = 57.5 square centimetres


Hope this helps.

[Peter Pedant]

beat me to it atheist
and the formula 'comes out' if you take the trap as two triangles
base - 4 and 19 ( or a and b)

[Prudie]

And that's the formula given in my google link and it's a damned sight easier to remember and use than this example that needs the areas of 2 triangles and a rectangle added together plus the area of one of the triangles needs pythagoras to work out the base and then some geometric logic to work out the base of the other triangle..how can that be easier to understand?

[ToraToraTora]

answer 4 had the correct answer.

[bobbinwales]

Thats fine prudie if your allowed to take your phone into an exam these days and use Google....maybe your allowed now, not a bad idea really as exams without phones are not measuring what we do in real life

[Atheist]

It seems to me that if the area of a rectangle is width times height then area of a trapezium is average width times height.
But, we all have different ways of seeing or visualising these things.
For those learning how to get answers, a simple formula is probably the best way to approach it.

[bobbinwales]

I hope basil updates tge best answerto someone else

[kuiperbelt]

johnny /make it into a rectangle then half the volume/
Oh Dear!!

TTT /A=(a+b)/2*h/
No wonder the kids don't have a chance!!