SOLUTION: a trapezium has a sides of 12, 12, 15 respectively and an [included] angle of 90°. find the surface area of the one side of the trapezium.

A four-sided polygon with exactly one pair of parallel sides is
called "a trapezoid" in US English and "a trapezium" in UK English.
One with sides 12, 12, 15 an [included] angle of 90° must be this: 



Since it has one [included] angle of 90° then it
must contain another one as well.

But these instructions make no sense:

"find the surface area of the one side of the trapezium."

"Surface area" is used for 3-dimensional figures, not 
2-dimensional figures.  And "sides" only have length, not
area.

Maybe you mean:

(a) "What is the length of the fourth side of the trapezium?"

and

(b) "What is the area of the trapezium?"

To answer those questions we draw in this green line
altitude, which also has length 12:



We calculate the bottom side of the right triangle
by using the Pythagorean theorem.








So the bottom side of the right triangle is 9.
The rest of the bottom side of the trapezium is the
same length as the top side of the trapezium or 12.



Therefore the bottom side of the trapezium is

12+9 or 21.

The area of the trapezoid can either be calculated
using the formula:



where a and b are the two parallel sides of the trapezium,
and h is the perpendicular distance between them:




Or else you can find the area of the square, which is 
12x12 = 144
and add the area of the right triangle, which is



And get 


Edwin