Question 843854
A drawing helps, and is difficult to do through this system; so here is a description of the drawing:


Let b = the shorter base.
Longer base is b+10.
Each nonparallel side of the trapezoid is 2b-3, and the trapezoid has two of them.


The perimeter is then {{{highlight_green(b+(b+10)+(2b-3)+(2b-3)=52)}}}.
Omitting the steps,... the solution here is {{{highlight(b=8)}}}.
The smaller base is 8 yards and the larger base is 18 yards.


Each nonparallel side, {{{-3+2*8=highlight(13)}}}.


Relabeling all four sides of this trapezoid, you can figure how it is composed of a rectangle and two congruent right triangles.  You want the HEIGHT of this entire figure.  Continue analyzing this figure:  the triangles each have 5 yard leg at the bottom, hypotenuse of 13, and unknown other leg, y.
We want this y, because this is the height of the figure:
{{{highlight_green(y^2+5^2=13^2)}}}.
{{{y=sqrt(13^2-5^2)}}}
{{{y=sqrt(169-25)}}}
{{{y=sqrt(144)}}}, ... {{{highlight(y=12)}}}.


AREA-------
(Average of the two bases) multiplied by (Altitude of the trapezoid)
Area, {{{highlight(highlight(((8+18)/2)*12))}}}
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13*12=156 square yards