To solve it I used the fact that the area of a rectangle is and I also used the distributive property which says
As the sides are and to find the area I multiplied them.
Surds act like any other number when multiplied and using the distributive property above for this case: and and
Therefore the area is
As a law of surds, for positive p,q:
You could leave the answer as but it is more usual to simplify.
To simplify a surd get the prime factors of the number inside it- in this case 50.
Using the rule directly above
because we can simplify the above to give which is fully simplified.
I then combined this with the first part (ab) and got the final answer of