The ratio of the area of square PQRS to the area of square ABCD is 5/9
<h3>Area of square ABCD</h3>Assume the measure of the side lengths of the square ABCD is 1, then the area of the square ABCD is:
See attachment for the diagram that represents the relationship between both squares.
<h3 /><h3>Pythagoras theorem</h3>The measure of length PQ is then calculated using the following Pythagoras theorem:
Evaluate the squares
Add the fractions
The above represents the area of the square PQRS.
i.e.
So, the ratio of the area of PQRS to ABCD is:
This gives
Hence, the ratio of the area of square PQRS to the area of square ABCD is 5/9
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