Question

pqrs is a square . if po = 4.5cm find pr and qs

Answer 1

Answer: 
We have a square PQRS in which two diagonals PR and QS intersect each other at O
And area of ∆POQ = 4 cm2

We know Area of PQRS = Area of ​∆POQ + Area of ​∆POS + Area of ​∆ROS + Area of ​∆ROQ
Since every square is a parallelogram and in every parallelogram, diagonals divide it into 4 triangles of equal areas, so
Area of ∆POQ =  Area of ​∆POS =  Area of ​∆ROS = Area of ​∆ROQ
And we know Area of ∆POQ = 4 cm2
So,
Area of ∆POQ =  Area of ​∆POS =  Area of ​∆ROS = Area of ​∆ROQ ​= 4 cm2
Then ​Area of PQRS = 4 + 4 + 4 + 4 = 16 cm2                     (Ans)

Answer 2

Po=4.5cm So,Po=or=oq=os=4.5cm Because, diagonals of square bisects each other. By using Pythagoras theorem, we get the side 6.36cm or 6.4cm. So,pr=qs=6.4cm