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Q: Can a square and a trapezoid ever have the same area and why?

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Basic answer: Yes.

Because a square has equal sides and a trapezoid doesn't, but at the same time they can have the same total but use different factors.

Yes

Yes. For example, if the square's side length was 10, the area would be 100. If the trapezoid's two base lengths were 5 and 20, and the height was 8, the area would be 100.

No.

-- You can make a square have any area you want it to, by making its sideslonger or shorter. You just have to keep all the sides the same length andone of its angles 90 degrees, otherwise you won't have a square any more.-- You can make a trapezoid have any area you want it to, by making its sideslonger or shorter. You just have to keep one pair of sides parallel, otherwiseyou won't have a trapezoid any more.-- Since you can make a square with any area you want, and you can make atrapezoid with any area you want, there's no reason why you can't make oneof each, that both have the same area.-- And while you're at it, you could also make a circle that has the same areaas the square and the trapezoid.

Yes.

A square.

Yes, certainly. The trapezoid area is one half sum of bases times height and the parallelogram area is base times height If the base of the parallelogram is equal to 1/2 the sum of he trapezoid bases, they have the same area

They are both polygons, they are both quadrilaterals, etc.

of course base times height for a square or rectangle. but for a trapezoid a= h x "b1+b2"

It is a square with a right angle triangle attached to it having the same height as the square.

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