Step 1: Find the length of .
Since is parallel to , we can find the length of by subtracting the length of from the length of .
Step 2: Find the length of .
Use Pythagoras' theorem, which states that the square of the length of a right-angled triangle's hypotenuse is equal to the sum of the squares of the lengths of the other two sides.
Substitute the known lengths in , and solve for the length of .
Step 3: Establish that quadrilateral is a rectangle.
is perpendicular to , so and are each equal to .
and are corresponding angles that are equal in measure, so is parallel to . Since is also parallel to , we know that quadrilateral is a parallelogram.
A parallelogram with a right angle must be a rectangle. Therefore, is a rectangle.
Step 4: Find the area of trapezium .
Add the area of and the area of rectangle .