# Maximal feild question

i added a photo of the situation

inside an ellipse (its formula x^2 /a^2 + y^2 /b^2 =1)
we block an isosceles trapeze .
the large base of the trapeze is on the X axes.

show that the maximal space of the trapeze is 3^0.5( a*b)?

i tried to get the feild of the trapeze by signing the height by X

but if i connect it to the ellipse formula for as x-b

i need another variable for the small base of the trapeze.

how can i solve it?

i tried by integrals but i dont know the formula of the trapeze fonction

what to do?
how do i prove that the maximal space of the trapeze is 3^0.5( a*b)?

plz help

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HallsofIvy
Homework Helper
Since the height is perpendicular to the x-axis, call it y instead!

What two x-values correspond to y? Their difference is the length of the smaller base.

there is no x vaules that are connected to the length of
the small base

we can say that the length of the big base is 2a
but in order to find the little base or the height of the trapeze
there begins the problem
notice that the answer includes only the parameters of the
ellipse fuction??
plz help

HallsofIvy
$$\frac{x^2}{a^2}+ \frac{y^2}{b^2}= 1$$