Can't figure this out... :(

Question

An isosceles trapezium with its longest side facing upward has an area of 145cm^2. Find the amount of material needed to make up the sides of the trapezium, when the side facing upward does not need to be covered (i.e. Perimeter - length of longest side).

I assume you'd sub 145 as the area into the trapezium area rule a= h((a+b)/2)
Or perhaps divide it into a rectangle and 2 triangles?? Any help appreciated!

Answer 1

I see no way to do this. All you know is the area. There are many isosceles trapezoids that can have such an area, each with a different perimeter.

For instance, if the height is 5, then (a+b)/2 = 29
and the slant sides are of length

s^2 = 5^2 + ((b-a)/2)^2

So, the perimeter can have many possible values. And that's just using h=5.

Something more needs to be nailed down.